JM Information Retrieval Techniques Unit II

Modern Information Retrieval
Chapter 3
Modeling
Part I: Classic Models
Introduction to IR Models
Basic Concepts
The Boolean Model
Term Weighting
The Vector Model
Probabilistic Model
p. 1

IR Models
Modeling in IR is a complex process aimed at
producing a ranking function
Ranking function: a function that assigns scores to documents
with regard to a given query
This process consists of two main tasks:
The conception of a logical framework for representing
documents and queries
The definition of a ranking function that allows quantifying the
similarities among documents and queries
p. 2

Modeling and Ranking
IR systems usually adopt index terms to index and
retrieve documents
Index term:
In a restricted sense: it is a keyword that has some meaning on
its own; usually plays the role of a noun
In a more general form: it is any word that appears in a
document
Retrieval based on index terms can be implemented
efficiently
Also, index terms are simple to refer to in a query
Simplicity is important because it reduces the effort of
query formulation
p. 3

Introduction
documents
information
need
Information retrieval process
index terms
match
ranking
3
1
2
...
docs terms
query terms
p. 4

Introduction
A ranking is an ordering of the documents that
(hopefully) reflects their relevance to a user query
Thus, any IR system has to deal with the problem of
predicting which documents the users will find relevant
This problem naturally embodies a degree of
uncertainty, or vagueness
p. 5

IR Models
An IR model is a quadruple [D, Q, F , R(qi, dj )]
where
1. D is a set of logical views for the documents in the collection
2. Q is a set of logical views for the user queries
3. F is a framework for modeling documents and queries
4. R(qi, dj ) is a ranking function
Q
D
q
d
R(d ,q
)
p. 6

Retrieval: Ad Hoc x Filtering
Ad Hoc Retrieval:
Collection
Q1 Q3
Q2
Q4
p. 8

Retrieval: Ad Hoc x Filtering
Filtering
documents stream
user 2
user 1
p. 9

Basic Concepts
Each document is represented by a set of
representative keywords or index terms
An index term is a word or group of consecutive words
in a document
A pre-selected set of index terms can be used to
summarize the document contents
However, it might be interesting to assume that all
words are index terms (full text representation)
p. 10

Basic Concepts
Let,
t be the number of index terms in the document collection
ki be a generic index term
Then,
The vocabulary V = {k1, . . . , kt} is the set of all distinct
index terms in the collection
p. 11
k k k k
V=

Basic Concepts
Documents and queries can be represented by
patterns of term co-occurrences
V=
Each of these patterns of term co-occurence is called a
term conjunctive component
For each document dj (or query q) we associate a
unique term conjunctive component c(dj ) (or c(q))
p. 12

The Term-Document Matrix
The occurrence of a term ki in a document dj
establishes a relation between ki and dj
A term-document relation between ki and dj can be
quantified by the frequency of the term in the document
In matrix form, this can written as
d1 d2
1,1
f1,2
p. 13
k1
k2
k3



f
f f
2,1
2,2
f3,1 f3,2



where each fi , j element stands for the frequency of
term ki in document dj

Basic Concepts
Logical view of a document: from full text to a set of
index terms
p. 14

The Boolean Model
Simple model based on set theory and boolean
algebra
Queries specified as boolean expressions
quite intuitive and precise semantics
neat formalism
example of query
q = ka ∧ (kb
∨ ¬kc)
Term-document frequencies in the term-document
matrix are all binary
wi j ∈ {0, 1}: weight associated with pair (ki, dj )
wiq ∈ {0, 1}: weight associated with pair (ki, q)
p. 16

The Boolean Model
A term conjunctive component that satisfies a query q is
called a query conjunctive component c(q)
A query q rewritten as a disjunction of those
components is called the disjunct normal form qDNF
To illustrate, consider
query q = ka ∧ (kb ∨ ¬kc)
vocabulary V = {ka, kb, kc}
Then
q DNF
= (1, 1, 1) ∨ (1, 1, 0) ∨ (1,
0, 0)
c(q): a conjunctive component for
q
p. 17

The Boolean Model
Kc
p. 18
The three conjunctive components for the query
q = ka ∧ (kb ∨ ¬kc)
Ka
Kb
(1,1,1)

The Boolean Model
This approach works even if the vocabulary of the
collection includes terms not in the query
Consider that the vocabulary is given by
V = {ka, kb, kc, kd}
Then, a document dj that contains only terms ka, kb,
and kc is represented by c(dj ) = (1, 1, 1, 0)
The query [q = ka
∧ (kb ∨ ¬kc)] is represented
in
p. 19
disjunctive normal form as
qDNF
= (1, 1, 1, 0) ∨ (1, 1, 1,
1) ∨
(1, 1, 0, 0) ∨ (1, 1, 0, 1)
∨
(1, 0, 0, 0) ∨ (1, 0, 0, 1)

The Boolean Model
The similarity of the document dj to the query q is
defined as
j
sim(d , q)
=
(
1 if ∃c(q) | c(q) =
c(dj )
0 otherwise
The Boolean model predicts that each document is
either relevant or non-relevant
p. 20

Drawbacks of the Boolean Model
Retrieval based on binary decision criteria with no
notion of partial matching
No ranking of the documents is provided (absence of a
grading scale)
Information need has to be translated into a Boolean
expression, which most users find awkward
The Boolean queries formulated by the users are most
often too simplistic
The model frequently returns either too few or too many
documents in response to a user query
p. 21

Term Weighting
The terms of a document are not equally useful for
describing the document contents
In fact, there are index terms which are simply vaguer
than others
There are properties of an index term which are useful
for evaluating the importance of the term in a document
For instance, a word which appears in all documents of a
collection is completely useless for retrieval tasks
p. 23

Term Weighting
To characterize term importance, we associate a weight
wi,j
> 0 with each term ki that occurs in the document
dj
If ki that does not appear in the document dj , then wi , j = 0.
The weight wi,j quantifies the importance of the index
term ki for describing the contents of document dj
These weights are useful to compute a rank for each
document in the collection with regard to a given query
p. 24

Term Weighting
Let,
ki be an index term and dj be a document
V = {k1, k2, ..., kt} be the set of all index terms
wi , j ≥ 0 be the weight associated with (ki, dj )
Then we define d→j = (w1,j, w2,j, ..., wt,j ) as a weighted
vector that contains the weight wi,j of each term ki ∈ V
in the document dj
k
k
k
.
k
w
w
w
.
w
V d
p. 25

Term Weighting
The weights wi,j can be computed using the frequencies
of occurrence of the terms within documents
Let fi , j be the frequency of occurrence of index term ki in
the document dj
The total frequency of occurrence Fi of term ki in the
collection is defined as
i
p. 26
N
Σ
F = f
j=1
i,j
where N is the number of documents in the collection

Term Weighting
The document frequency ni of a term ki is the number
of documents in which it occurs
Notice that ni ≤ Fi.
For instance, in the document collection below, the
values fi , j , Fi and ni associated with the term do
are
f (do, d1) =
2 f (do, d2)
= 0 f (do,
d3) = 3 f
(do, d4) = 3
F (do) = 8
n(do) = 3
To do is to be.
To be is to do. To be or not to be.
I am what I am.
I think therefore I am.
Do be do be do.
d1
d2
d3
Do do do, da da da.
Let it be, let it be.
p. 27
d4

Term-term correlation matrix
For classic information retrieval models, the index term
weights are assumed to be mutually independent
This means that wi , j tells us nothing about wi+1,j
This is clearly a simplification because occurrences of
index terms in a document are not uncorrelated
For instance, the terms computer and network tend to
appear together in a document about computer
networks
In this document, the appearance of one of these terms attracts
the appearance of the other
Thus, they are correlated and their weights should reflect this
correlation.
p. 28

To take into account term-term correlations, we can
compute a correlation matrix
Let M→ = (mi j ) be a term-document matrix t × N
where
m ij = wi,j
The matrix C→ = M→ M→ t is a term-term
correlation matrix
u,v
c
=
Each element cu,v ∈ C expresses a correlation between
terms ku and kv, given by
Σ
dj
wu,j × wv,j
Higher the number of documents in which the terms ku
and kv co-occur, stronger is this correlation
p. 29

Term-term correlation matrix for a sample collection
d1 d2 k1 k2 k3
k1
k2
k3




w
w
1,1 w1,2
2,1 w2,2
w3,1 w3,2
M




1
d
d2
"
w1,1 w2,1 w3,1
w1,2 w2,2 w3,2
M T
#
×
` ˛
¸
x
p. 30
⇓
k2
w1,1w2,1 + w1,2w2,2
w2,1w2,1 + w2,2w2,2
w3,1w2,1 + w3,2w2,2
k3
k1
k2
k3




w1,1w1,1
k1
+ w
w
1,2 1,2
w1,1w3,1 + w1,2w3,2
w2,1w3,1 + w2,2w3,2
w3,1w3,1 + w3,2w3,2
w2,1w1,1
+ w w
2,2 1,2
w3,1w1,1 + w3,2w1,2





TF-IDF Weights
TF-IDF term weighting scheme:
Term frequency (TF)
Inverse document frequency (IDF)
Foundations of the most popular term weighting scheme in IR
p. 32

Luhn Assumption. The value of wi,j is proportional to
the term frequency fi , j
That is, the more often a term occurs in the text of the document,
the higher its weight
This is based on the observation that high frequency
terms are important for describing documents
Which leads directly to the following tf weight
formulation:
tfi,j = fi,j
p. 33

Term Frequency (TF) Weights
A variant of tf weight used in the literature is
i,j
tf
=
(
i,j
f i,j
1 + log f if > 0
0 otherwise
where the log is taken in base 2
The log expression is a the preferred form because it
makes them directly comparable to idf weights, as we
later discuss
p. 34

Term Frequency (TF) Weights
Log tf weights tfi , j for the example collection
Vocabulary
1 to
2 do
3 is
4 be
5 or
6 not
7 I
8 am
9 what
10 think
11 therefore
12 da
13 let
14 it
tfi,1 tfi,2 tfi,3 tfi,4
3 2 - -
2 - 2.585 2.585
2 - - -
2 2 2 2
- 1 - -
- 1 - -
- 2 2 -
- 2 1 -
- 1 - -
- - 1 -
- - 1 -
- - - 2.585
- - - 2
- - - 2
p. 35

Inverse Document Frequency
We call document exhaustivity the number of index
terms assigned to a document
The more index terms are assigned to a document, the
higher is the probability of retrieval for that document
If too many terms are assigned to a document, it will be retrieved
by queries for which it is not relevant
Optimal exhaustivity. We can circumvent this problem
by optimizing the number of terms per document
Another approach is by weighting the terms differently,
by exploring the notion of term specificity
p. 36

Specificity is a property of the term semantics
A term is more or less specific depending on its meaning
To exemplify, the term beverage is less specific than the
terms tea and beer
We could expect that the term beverage occurs in more
documents than the terms tea and beer
Term specificity should be interpreted as a statistical
rather than semantic property of the term
Statistical term specificity. The inverse of the number
of documents in which the term occurs
p. 37

Terms are distributed in a text according to Zipf’s Law
Thus, if we sort the vocabulary terms in decreasing
order of document frequencies we have
n(r) ∼ r−α
where n(r) refer to the rth largest document frequency
and α is an empirical constant
That is, the document frequency of term ki is an
exponential function of its rank.
n(r) = Cr− α
where C is a second empirical constant
p. 38

Setting α = 1 (simple approximation for
english collections) and taking logs we have
log n(r) = log C − log r
For r = 1, we have C = n(1), i.e., the value of C is
the largest document frequency
This value works as a normalization constant
An alternative is to do the normalization assuming
C = N , where N is the number of docs in the
collection
log r ∼ log N − log n(r)
p. 39

Let ki be the term with the rth largest document
frequency, i.e., n(r) = ni. Then,
N
idfi = log
ni
where idfi is called the inverse document frequency
of term ki
Idf provides a foundation for modern term weighting
schemes and is used for ranking in almost all IR
systems
p. 40

Idf values for example collection
term ni idfi = log(N/ni)
1 to 2 1
2 do 3 0.415
3 is 1 2
4 be 4 0
5 or 1 2
6 not 1 2
7 I 2 1
8 am 2 1
9 what 1 2
10 think 1 2
11 therefore 1 2
12 da 1 2
13 let 1 2
14 it 1 2
p. 41

TF-IDF weighting scheme
The best known term weighting schemes use weights
that combine idf factors with term frequencies
Let wi,j be the term weight associated with the term ki
and the document dj
Then, we define
wi,j =
p. 42
(
(1 + log fi , j ) ×
log
if
f i,j
>
0
N
ni
0
otherwise
which is referred to as a tf-idf weighting scheme

TF-IDF weighting scheme
Tf-idf weights of all terms present in our example
document collection
d1 d2 d3 d4
1 to 3 2 - -
2 do 0.830 - 1.073 1.073
3 is 4 - - -
4 be - - - -
5 or - 2 - -
6 not - 2 - -
7 I - 2 2 -
8 am - 2 1 -
9 what - 2 - -
10 think - - 2 -
11 therefore - - 2 -
12 da - - - 5.170
13 let - - - 4
14 it - - - 4
p. 43

Variants of TF-IDF
Several variations of the above expression for tf-idf
weights are described in the literature
For tf weights, five distinct variants are illustrated
below
tf weight
binary {0,1}
raw frequency f i , j
log normalization 1 + log fi , j
double normalization 0.5 0.5 + 0.5 f i , j
m a x i f i , j
double normalization K f i , j
K + (1 − K) m a x i f i , j
p. 44

Variants of TF-IDF
Five distinct variants of idf weight
idf weight
unary 1
inverse frequency log N
n i
inv frequency smooth log(1 + N
)
n i
inv frequeny max log(1 +
m a x i n i
)
n i
probabilistic inv frequency log N − n i
n i
p. 45

Variants of TF-IDF
Recommended tf-idf weighting schemes
p. 46
weighting scheme document term weight query term weight
1
N
fi , j ∗ log n i
(0.5 + 0.5 f i , q
) ∗ log
N
m a x i
f i , q n i
2 1 + log fi , j
log(1 + N
)
n i
3
N
(1 + log fi , j ) ∗
log n i
N
(1 + log fi , q ) ∗
log n i

TF-IDF Properties
Consider the tf, idf, and tf-idf weights for the Wall Street
Journal reference collection
To study their behavior, we would like to plot them
together
While idf is computed over all the collection, tf is
computed on a per document basis. Thus, we need a
representation of tf based on all the collection, which is
provided by the term collection frequency Fi
This reasoning leads to the following tf and idf term
weights:
N
Σ
p. 47
tf = 1 + log f
i i,j
j=1
i
N
idf = log
ni

TF-IDF Properties
Plotting tf and idf in logarithmic scale yields
We observe that tf and idf weights present power-law
behaviors that balance each other
The terms of intermediate idf values display maximum
tf-idf weights and are most interesting for ranking
p. 48

Document Length Normalization
Document sizes might vary widely
This is a problem because longer documents are more
likely to be retrieved by a given query
To compensate for this undesired effect, we can divide
the rank of each document by its length
This procedure consistently leads to better ranking, and
it is called document length normalization
p. 49

Methods of document length normalization depend on the
representation adopted for the documents:
Size in bytes: consider that each document is represented
simply as a stream of bytes
Number of words: each document is represented as a single
string, and the document length is the number of words in it
Vector norms: documents are represented as vectors of
weighted terms
p. 50

Documents represented as vectors of weighted terms
Each term of a collection is associated with an orthonormal unit
vector →ki in a t-dimensional space
For each term ki of a document dj is associated the term
vector component wi , j × →ki
p. 51

The document representation d→j is a vector
composed of all its term vector components
d→j = (w1,j, w2,j, ..., wt,j )
The document length is given by the norm of this vector,
which is computed as follows
,
|d→j |
=
t
p. 52
u Σ
, w2
i
i,j

Three variants of document lengths for the example
collection
d1 d2 d3 d4
size in bytes 34 37 41 43
number of words 10 11 10 12
vector norm 5.068 4.899 3.762 7.738
p. 53

The Vector Model
Boolean matching and binary weights is too limiting
The vector model proposes a framework in which
partial matching is possible
This is accomplished by assigning non-binary weights
to index terms in queries and in documents
Term weights are used to compute a degree of
similarity between a query and each document
The documents are ranked in decreasing order of their
degree of similarity
p. 55

The Vector Model
For the vector model:
The weight wi , j associated with a pair (ki, dj ) is positive
and non-binary
The index terms are assumed to be all mutually
independent
They are represented as unit vectors of a t-dimensionsal space (t
is the total number of index terms)
The representations of document dj and query q are
t-dimensional vectors given by
d→j = (w1j, w2j, . . . , wt j )
→q = (w1q, w2q, . . . , wtq )
p. 56

The Vector Model
Similarity between a document dj and a query q
j
i
d
q
cos(θ)
=
d→j
•→q
|d→j |×|
→q|
j
sim(d , q)
=
Σ t
i=1 i,j
w ×wi,q
q Σ t
i=1 w2
i,j ×
q Σ t
j=1 w2
i,q
Since wij > 0 and wiq > 0, we have 0 ≤ sim(dj , q) ≤
1
p. 57

The Vector Model
Weights in the Vector model are basically tf-idf weights
wi,q
N
= (1 + log fi, q ) ×
log
n
i
wi,j
N
= (1 + log fi , j ) ×
log
n
i
These equations should only be applied for values of
term frequency greater than zero
If the term frequency is zero, the respective weight is
also zero
p. 58

The Vector Model
Document ranks computed by the Vector model for the
query “to do” (see tf-idf weight values in Slide 43)
doc rank computation rank
d1
1∗3+0.415∗0.830
5.068
0.660
d2
1∗2+0.415∗0
4.899
0.408
d3
1∗0+0.415∗1.073
3.762
0.118
d4
1∗0+0.415∗1.073
7.738
0.058
p. 59

The Vector Model
Advantages:
term-weighting improves quality of the answer set
partial matching allows retrieval of docs that approximate the
query conditions
cosine ranking formula sorts documents according to a degree of
similarity to the query
document length normalization is naturally built-in into the
ranking
Disadvantages:
It assumes independence of index terms
p. 60

Probabilistic Model
The probabilistic model captures the IR problem using a
probabilistic framework
Given a user query, there is an ideal answer set for
this query
Given a description of this ideal answer set, we could
retrieve the relevant documents
Querying is seen as a specification of the properties of
this ideal answer set
But, what are these properties?
p. 62

Probabilistic Model
An initial set of documents is retrieved somehow
The user inspects these docs looking for the relevant
ones (in truth, only top 10-20 need to be inspected)
The IR system uses this information to refine the
description of the ideal answer set
By repeating this process, it is expected that the
description of the ideal answer set will improve
p. 63

Probabilistic Ranking Principle
The probabilistic model
Tries to estimate the probability that a document will be relevant
to a user query
Assumes that this probability depends on the query and
document representations only
The ideal answer set, referred to as R, should maximize the
probability of relevance
But,
How to compute these probabilities?
What is the sample space?
p. 64

The Ranking
Let,
R be the set of relevant documents to query q
R be the set of non-relevant documents to query q
P (R|d→j ) be the probability that dj is relevant to the
query q P (R|d→j ) be the probability that dj is non-
relevant to q
The similarity sim(dj , q) can be defined as
j
sim(d , q) =
→
P (R|
d
j )
j
p. 65
P (R|
d→ )

The Ranking
Using Bayes’ rule,
j
sim(d , q)
=
→
j
P (d
|
R, q) × P (R,
q)
j
P (d→ |R, q) × P
(R, q)
~ P (d→j |R,
q) j
P (d→ |R,
q)
where
P (d→j |R, q) : probability of randomly selecting the
document
dj from the set R
P (R, q) : probability that a document randomly selected
from the entire collection is relevant to query q
P (d→j |R, q) and P (R, q) : analogous and
complementary
p. 66

The Ranking
Assuming that the weights wi,j are all binary and
assuming independence among the index terms:
j
sim(d , q)
∼
( i i,j
k |w =1 i
P (k |R, q)) ×
(
Q Q
i i,j
k |w =0 i
P (k |R,
q))
(
Q
ki |wi , j =1 i
P (k
|
R, q)) ×
(
Q
ki |wi , j =0 i
P (k |R,
q))
where
P (ki|R, q): probability that the term ki is present in
a document randomly selected from the set R
P (ki|R, q): probability that ki is not present in a
document randomly selected from the set R
probabilities with R: analogous to the ones just described
p. 67

The Ranking
Taking logarithms, we write
p. 69
sim(dj , q) ∼
log
Y
ki |wi , j =1
piR +
log
Y
ki |wi , j =0
(1 −
piR)
—
log
Y
ki |wi , j =1
qiR −
log
Y
ki |wi , j =0
(1 −
qiR)

The Ranking
Using logarithm operations, we obtain
sim(dj , q) ∼
log
Y
ki |wi , j =1
piR
(1 −
piR)
+
log
Y
ki
iR
(1 − p
)
+
log
Y
ki |wi , j =1
iR
(1 − q
)
qiR
—
log
Y
ki
iR
(1 − q
)
Notice that two of the factors in the formula above are a
function of all index terms and do not depend on
document dj . They are constants for a given query and
can be disregarded for the purpose of ranking
p. 71

The Ranking
Further, assuming that
6 ki /
∈
q,
piR = qiR
and converting the log products into sums of logs, we
finally obtain
sim(dj ,
q)
~
Σ
ki∈q∧ki∈dj
lo
g
pi R
1−pi R
+
log
1−qi R
qiR
which is a key expression for ranking computation in the
probabilistic model
p. 72

Term Incidence Contingency Table
Let,
N be the number of documents in the collection
ni be the number of documents that contain term ki
R be the total number of relevant documents to query q
ri be the number of relevant documents that contain term ki
Based on these variables, we can build the following
contingency table
relevant non-relevant all docs
docs that contain ki ri ni − ri ni
docs that do not contain ki R − ri N − ni − (R − ri) N − ni
all docs R N − R N
p. 73

Ranking Formula
iR
p
=
If information on the contingency table were available
for a given query, we could write
ri
R
qiR = ni −ri
N −R
Then, the equation for ranking computation in the
probabilistic model could be rewritten as
Σ
sim(dj , q) ~ log
ki[q,dj ]
×
ri N − n − R +
r
i i
R − ri ni − ri
p. 74
where ki[q, dj ] is a short notation for ki ∈ q ∧ ki ∈
dj

Ranking Formula
In the previous formula, we are still dependent on an
estimation of the relevant dos for the query
For handling small values of ri, we add 0.5 to each
of the terms in the formula above, which changes
sim(dj , q) into
Σ
ki[q,dj ]
i i
ri + 0.5 N − n − R + r +
0.5
R − ri + 0.5 ni − ri +
0.5
log ×
This formula is considered as the classic ranking
equation for the probabilistic model and is known as the
Robertson-Sparck Jones Equation
p. 75

Ranking Formula
The previous equation cannot be computed without
estimates of ri and R
One possibility is to assume R = ri = 0, as a way
to boostrap the ranking equation, which leads to
j
sim(d , q)
~
Σ
ki[q,dj ] lo
g
i
N −n +0.5
ni+0.5
This equation provides an idf-like ranking computation
In the absence of relevance information, this is the
equation for ranking in the probabilistic model
p. 76

Ranking Example
Document ranks computed by the previous probabilistic
ranking equation for the query “to do”
d1
log 4−2+0.5 + log 4−3+0.5
2+0.5
3+0.5
- 1.222
d2
log 4−2+0.5
2+0.5
0
d3
log 4−3+0.5
3+0.5
- 1.222
d4
log 4−3+0.5
3+0.5
- 1.222
p. 77

Ranking Example
The ranking computation led to negative weights
because of the term “do”
Actually, the probabilistic ranking equation produces
negative terms whenever ni > N/2
One possible artifact to contain the effect of negative
weights is to change the previous equation to:
Σ
sim(dj , q) ~
log ki[q,dj ]
N +
0.5
ni +
0.5
By doing so, a term that occurs in all documents
(ni = N ) produces a weight equal to zero
p. 78

Ranking Example
Using this latest formulation, we redo the ranking
computation for our example collection for the query “to
do” and obtain
d1
log 4+0.5 + log 4+0.5
2+0.5
3+0.5
1.210
d2
log 4+0.5
2+0.5
0.847
d3
log 4+0.5
3+0.5
0.362
d4
log 4+0.5
3+0.5
0.362
p. 79

Estimaging ri and R
Our examples above considered that ri = R = 0
An alternative is to estimate ri and R performing an
initial search:
select the top 10-20 ranked documents
inspect them to gather new estimates for ri and R
remove the 10-20 documents used from the collection
rerun the query with the estimates obtained for ri and R
Unfortunately, procedures such as these require human
intervention to initially select the relevant documents
p. 80

Improving the Initial Ranking
Consider the equation
sim(dj , q) ~
Σ
ki∈q∧ki∈dj
log
piR
1 − piR
+
log
1 −
q
iR
qiR
How obtain the probabilities piR and qiR ?
Estimates based on assumptions:
pi R = 0.5
n i
N
qi R = where ni is the number of docs that contain ki
Use this initial guess to retrieve an initial ranking
Improve upon this initial ranking
p. 81

Substituting piR and qiR into the previous Equation, we
obtain:
Σ
sim(dj , q) ~
log ki∈q∧ki∈dj
N − ni
ni
That is the equation used when no relevance
information is provided, without the 0.5 correction factor
Given this initial guess, we can provide an initial
probabilistic ranking
After that, we can attempt to improve this initial ranking
as follows
p. 82

iR
p
=
We can attempt to improve this initial ranking as follows
Let
D : set of docs initially retrieved
Di : subset of docs retrieved that contain ki
Reevaluate estimates:
D i
D
qiR = ni −Di
N −D
This process can then be repeated recursively
p. 83

sim(dj , q) ~
Σ
ki∈q∧ki∈dj
lo
g
N − ni
ni
To avoid problems with D = 1 and Di =
0:
iR
D +
1
Di + 0.5
p = ;
q
iR
ni − Di +
0.5
= N − D +
1
Also,
p. 84
Di + n i
D +
1
piR =
N ;
i i
n − D
+
ni
qiR = N
N − D +
1

Pluses and Minuses
Advantages:
Docs ranked in decreasing order of probability of
relevance
Disadvantages:
need to guess initial estimates for piR
method does not take into account tf factors
the lack of document length normalization
p. 85

Comparison of Classic Models
Boolean model does not provide for partial matches
and is considered to be the weakest classic model
There is some controversy as to whether the
probabilistic model outperforms the vector model
Croft suggested that the probabilistic model provides a
better retrieval performance
However, Salton et al showed that the vector model
outperforms it with general collections
This also seems to be the dominant thought among
researchers and practitioners of IR.
p. 86

Modeling
Part II: Alternative Set and Vector
Models
Set-Based Model
Extended Boolean Model
Fuzzy Set Model
The Generalized Vector
Model
Latent Semantic Indexing
Neural Network for IR
p. 87

Alternative Set Theoretic Models
Set-Based Model
Fuzzy Set Model
p. 88

Set-Based Model
This is a more recent approach (2005) that combines
set theory with a vectorial ranking
The fundamental idea is to use mutual dependencies
among index terms to improve results
Term dependencies are captured through termsets,
which are sets of correlated terms
The approach, which leads to improved results with
various collections, constitutes the first IR model that
effectively took advantage of term dependence with
general collections
p. 90

Termsets
Termset is a concept used in place of the index terms
A termset Si = {ka, kb, ..., kn} is a subset of the terms in
the collection
If all index terms in Si occur in a document dj then we
say that the termset Si occurs in dj
There are 2t termsets that might occur in the
documents of a collection, where t is the vocabulary
size
However, most combinations of terms have no semantic meaning
Thus, the actual number of termsets in a collection is far smaller
than 2t
p. 91

Termsets
Let t be the number of terms of the collection
Then, the set VS = {S1, S2, ..., S2t } is the vocabulary-
set
of the collection
To illustrate, consider the document collection below
To do is to be.
To be is to do. To be or not to be.
I am what I am.
I think therefore I am.
Do be do be do.
d1
d2
d3
Do do do, da da da.
Let it be, let it be.
p. 92
d4

Termsets
To simplify notation, let us define
ka = to kd = be kg = I kj = think km = let
kb = do ke = or kh = am kk = therefore kn = it
kc = is kf = not ki = what kl = da
Further, let the letters a...n refer to the index terms
ka...kn , respectively
a d e f a d
g h i g h
a b c a d
a d c a b
d
1
g j k g h
b d b d b
d3
d2
b b b l l l
m n d m n d
p. 93
d4

Termsets
Consider the query q as “to do be it”, i.e. q = {a, b, d,
n}
For this query, the vocabulary-set is as below
Termset Set of Terms Documents
Sa {a} {d1 , d2}
Sb {b} {d1 , d3 , d4}
Sd {d} {d1 , d2 , d3 , d4}
Sn {n} {d4 }
Sab
{a, b} {d1 }
Sad
{a, d} {d1 , d2}
Sbd
{b, d} {d1 , d3 , d4}
Sbn
{b, n} {d4 }
Sabd
{a, b, d} {d1 }
Sbdn
{b, d, n} {d4 }
p. 94
Notice that there are
11 termsets that occur
in our collection, out
of the maximum of 15
termsets that can be
formed with the terms
in q

Termsets
At query processing time, only the termsets generated
by the query need to be considered
A termset composed of n terms is called an n-termset
Let Ni be the number of documents in which Si occurs
An n-termset Si is said to be frequent if Ni is greater
than or equal to a given threshold
This implies that an n-termset is frequent if and only if all of its
(n − 1)-termsets are also frequent
Frequent termsets can be used to reduce the number of
termsets to consider with long queries
p. 95

Termsets
Let the threshold on the frequency of termsets be 2
To compute all frequent termsets for the query
q = {a, b, d, n} we proceed as follows
1. Compute the frequent 1-termsets and their inverted lists:
Sa = {d1, d2}
Sb = {d1, d3, d4}
Sd = {d1, d2, d3, d4}
2. Combine the inverted
lists to compute
frequent 2-termsets:
Sa d = {d1, d2}
Sbd = {d1, d3,
d4}
3. Since there are no frequent 3-
termsets, stop
a d e f a d
g h i g h
a b c a d
a d c a b
d
1
g j k g h
b d b d b
d2
d3
b b b l l l
m n d m n d
d4
p. 96

Termsets
Notice that there are only 5 frequent termsets in our
collection
Inverted lists for frequent n-termsets can be computed
by starting with the inverted lists of frequent 1-termsets
Thus, the only indice that is required are the standard inverted
lists used by any IR system
This is reasonably fast for short queries up to 4-5
terms
p. 97

Ranking Computation
The ranking computation is based on the vector model,
but adopts termsets instead of index terms
Given a query q, let
{S1, S2, . . .} be the set of all termsets originated from q
Ni be the number of documents in which termset Si occurs
N be the total number of documents in the collection
Fi , j be the frequency of termset Si in document dj
For each pair [Si, dj ] we compute a weight Wi , j given
by
Wi,j =
(
i,j
(1 + log F ) log(1
+ 0
N
Ni
) if Fi , j >
0
Fi , j = 0
We also compute a Wi,q value for each pair [Si,
q]
p. 98

Ranking Computation
Consider
query q = {a, b, d, n}
document d1 = ‘‘a b c a d a d c a b’’
Termset Weight
Sa
Sb
Sd
Sn
Sab
Sad
Sbd
Sbn
Sdn
Wa,1
Wb,1
Wd,1
Wn,1
Wab,1
Wad,1
Wbd,1
Wbn,1
p. 99
(1 + log 4) ∗ log(1 + 4/2) = 4.75
(1 + log 2) ∗ log(1 + 4/3) = 2.44
(1 + log 2) ∗ log(1 + 4/4) = 2.00
0 ∗ log(1 + 4/1) = 0.00
(1 + log 2) ∗ log(1 + 4/1) = 4.64
(1 + log 2) ∗ log(1 + 4/2) = 3.17
(1 + log 2) ∗ log(1 + 4/3) = 2.44
0 ∗ log(1 + 4/1) = 0.00
0 ∗ log(1 + 4/1) = 0.00
(1 + log 2) ∗ log(1 + 4/1) = 4.64
0 ∗ log(1 + 4/1) = 0.00

Ranking Computation
A document dj and a query q are represented as
vectors in a 2t-dimensional space of termsets
d→j = (W1 , j , W2,j, . .
. , W2t ,j )
→q = (W1,q, W2,q, .
. . , W2t,q )
The rank of dj to the query q is computed as
follows
j
sim(d , q)
=
d→j •
→q
|d→ | ×
|→q|
=
j j
Σ
Si i,j
W × Wi,q
|d→ | ×
|→q|
For termsets that are not in the query q, Wi,q = 0
p. 100

Ranking Computation
The document norm |d→j | is hard to compute in
the
space of termsets
Thus, its computation is restricted to 1-termsets
Let again q = {a, b, d, n} and d1
The document norm in terms of 1-termsets is
given by
q
|d→1| = W
2
a,1 + W2 2
+ W + W2
b,1 c,1 d,1
√
=
4.75
p. 101
2
+ 2.442 + 4.642 +
2.002
=
7.35

Ranking Computation
To compute the rank of d1, we need to consider the
seven termsets Sa, Sb, Sd, Sab, Sad, Sbd, and Sabd
The rank of d1 is then given by
sim(d1, q)
=
p. 102
(Wa,1 ∗ Wa,q + Wb,1 ∗ Wb,q + Wd,1 ∗ Wd,q + Wab,1
∗ Wab,q + Wad,1 ∗ Wad,q + Wbd,1 ∗ Wbd,q + Wabd,1
∗ Wabd,q ) /|d→1|
= (4.75 ∗ 1.58 + 2.44 ∗ 1.22 + 2.00 ∗ 1.00
+
4.64 ∗ 2.32 + 3.17 ∗ 1.58 + 2.44 ∗ 1.22 +
4.64 ∗ 2.32)/7.35
= 5.71

Closed Termsets
The concept of frequent termsets allows simplifying the
ranking computation
Yet, there are many frequent termsets in a large
collection
The number of termsets to consider might be prohibitively high
with large queries
To resolve this problem, we can further restrict the
ranking computation to a smaller number of termsets
This can be accomplished by observing some
properties of termsets such as the notion of closure
p. 103

Closed Termsets
The closure of a termset Si is the set of all frequent
termsets that co-occur with Si in the same set of docs
Given the closure of Si , the largest termset in it is called
a closed termset and is referred to as Φi
We formalize, as follows
Let Di ⊆ C be the subset of all documents in which termset Si
occurs and is frequent
Let S(Di ) be a set composed of the frequent termsets that occur
in all documents in Di and only in those
p. 104

Closed Termsets
Then, the closed termset SΦi satisfies the following
property
/ ESj ∈ S(Di ) | SΦi ⊂ Sj
Frequent and closed termsets for our example
collection, considering a minimum threshold equal to 2
frequency(Si) frequent termset closed termset
4 d d
3 b, bd bd
2 a, ad ad
2 g, h, gh, ghd ghd
p. 105

Closed Termsets
Closed termsets encapsulate smaller termsets
occurring in the same set of documents
The ranking sim(d1, q) of document d1 with regard
to query q is computed as follows:
d1 =’’a b c a d a d c a b ’’
q = {a, b, d, n}
minimum frequency threshold = 2
p. 106
sim(d1, q)
=
(Wd,1 ∗ Wd,q + Wab,1 ∗ Wab,q + Wad,1 ∗ Wad,q +
Wbd,1 ∗ Wbd,q + Wabd,1 ∗ Wabd,q )/|d→1|
= (2.00 ∗ 1.00 + 4.64 ∗ 2.32 + 3.17 ∗ 1.58
+
2.44 ∗ 1.22 + 4.64 ∗ 2.32)/7.35
= 4.28

Closed Termsets
Thus, if we restrict the ranking computation to closed
termsets, we can expect a reduction in query time
Smaller the number of closed termsets, sharper is the
reduction in query processing time
p. 107

In the Boolean model, no ranking of the answer set is
generated
One alternative is to extend the Boolean model with the
notions of partial matching and term weighting
This strategy allows one to combine characteristics of
the Vector model with properties of Boolean algebra
p. 109

The Idea
Consider a conjunctive Boolean query given by
q = kx ∧ ky
For the boolean model, a doc that contains a single
term of q is as irrelevant as a doc that contains none
However, this binary decision criteria frequently is not
in accordance with common sense
An analogous reasoning applies when one considers
purely disjunctive queries
p. 110

The Idea
When only two terms x and y are considered, we can
plot queries and docs in a two-dimensional space
A document dj is positioned in this space through the
adoption of weights wx, j and wy,j
p. 111

The Idea
These weights can be computed as normalized tf-idf
factors as follows
x,j
w
=
f x,j
maxx f x,j
×
idfx
maxi idfi
where
fx , j is the frequency of term kx in document dj
idfi is the inverse document frequency of term ki , as before
To simplify notation, let
wx , j = x and wy , j = y
d→j = (wx , j , wy , j ) as the point dj = (x, y)
p. 112

The Idea
For a disjunctive query qor = kx ∨ ky, the point (0, 0)
is
the least interesting one
This suggests taking the distance from (0, 0) as
a measure of similarity
sim(qor, d)
=
r
2
x +
y
2
2
p. 113

The Idea
For a conjunctive query qand = kx ∧ ky, the point (1, 1)
is
the most interesting one
This suggests taking the complement of the distance
from the point (1, 1) as a measure of similarity
sim(qa n d , d) = 1
−
r
(1 −
x)
2 + (1 −
y)
2
2
p. 114

The Idea
sim(qor, d)
=
r
2
x +
y
2
2
sim(qand, d) = 1
−
r
(1 −
x)
2 + (1 −
y)
2
2
p. 115

Generalizing the Idea
We can extend the previous model to consider
Euclidean distances in a t-dimensional space
This can be done using p-norms which extend the notion
of distance to include p-distances, where 1 ≤ p ≤ ∞
A generalized conjunctive query is given by
qand = k1 ∧p ∧p
k2 . . . ∧p
km
A generalized disjunctive query is given by
∨p ∨p
p. 116
qor = k1 k2 . . . ∨p km

Generalizing the Idea
The query-document similarities are now given by
or j
sim(q , d )
=
p p p
x1 +x2 +...+xm
m
1
p
sim(qand, dj ) = 1
−
1 2 m
(1−x ) +(1−x ) +...+(1−x )
p p p
m
1
p
where each xi stands for a weight wi,d
If p = 1 then (vector-like)
j
sim(qor, dj ) = sim(qand, d )
=
1
x +...+xm
m
If p = ∞ then (Fuzzy like)
sim(qor, dj ) = max(xi)
sim(qand, dj ) =
min(xi )
p. 117

Properties
By varying p, we can make the model behave as a
vector, as a fuzzy, or as an intermediary model
The processing of more general queries is done by
grouping the operators in a predefined order
For instance, consider the query q = (k1 ∧p k2) ∨p k3
k1 and k2 are to be used as in a vectorial retrieval
while the presence of k3 is required
The similarity sim(q, dj ) is computed as

sim(q, d) =
1
−
1
p
2
(1−x ) +(1−x )p
2
1
p
p
 
+ x
p
3
2



1
p
p. 118

Conclusions
Model is quite powerful
Properties are interesting and might be useful
Computation is somewhat complex
However, distributivity operation does not hold for
ranking computation:
q1 = (k1 V k2) Λ k3
q2 = (k1 Λ k3) V (k2 Λ k3)
sim(q1, dj ) /= sim(q2, dj )
p. 119

Fuzzy Set Model
Matching of a document to a query terms is
approximate or vague
This vagueness can be modeled using a fuzzy
framework, as follows:
each query term defines a fuzzy set
each doc has a degree of membership in
this set
This interpretation provides the foundation for many IR
models based on fuzzy theory
In here, we discuss the model proposed by
Ogawa, Morita, and Kobayashi
p. 121

Fuzzy Set Theory
Fuzzy set theory deals with the representation of
classes whose boundaries are not well defined
Key idea is to introduce the notion of a degree of
membership associated with the elements of the class
This degree of membership varies from 0 to 1 and
allows modelling the notion of marginal membership
Thus, membership is now a gradual notion, contrary to
the crispy notion enforced by classic Boolean logic
p. 122

Fuzzy Set Theory
A fuzzy subset A of a universe of discourse U is
characterized by a membership function
µA : U → [0, 1]
This function associates with each element u of U a
number µA(u) in the interval [0, 1]
The three most commonly used operations on fuzzy
sets are:
the complement of a fuzzy set
the union of two or more fuzzy sets
the intersection of two or more fuzzy sets
p. 123

Fuzzy Set Theory
Let,
U be the universe of discourse
A and B be two fuzzy subsets of U
A be the complement of A relative to U
u be an element of U
Then,
µA(u) = 1 − µA(u)
µA ∪ B (u) = max(µA(u), µB
(u))
µA ∩ B (u) = min(µA(u), µB (u))
p. 124

Fuzzy Information Retrieval
Fuzzy sets are modeled based on a thesaurus, which
defines term relationships
A thesaurus can be constructed by defining a term-term
correlation matrix C
Each element of C defines a normalized correlation
factor ci,l between two terms ki and kl
i,l
c
=
ni,l
ni + nl − ni,l
where
ni : number of docs which contain ki
nl : number of docs which contain kl
ni , l : number of docs which contain
both ki and kl
p. 125

i,j
µ = 1
−
We can use the term correlation matrix C to associate a
fuzzy set with each index term ki
In this fuzzy set, a document dj has a degree of
membership µi,j given by
Y
kl ∈ dj
(1 −
ci,l)
The above expression computes an algebraic sum over
all terms in dj
A document dj belongs to the fuzzy set associated with
ki, if its own terms are associated with ki
p. 126

If dj contains a term kl which is closely related to ki, we
have
~
1
ci,l
µi,j
~
1
and ki is a good fuzzy index for dj
p. 127

Fuzzy IR: An Example
Da
Db
cc cc
cc
D = cc + cc + cc
q 1 2
3
Dc
Consider the query q = ka
Λ
(kb
V ¬kc)
The disjunctive normal form of q is composed of 3
conjunctive components (cc), as follows:
→qdnf = (1, 1, 1) + (1, 1, 0) + (1, 0, 0) = cc1 +
cc2 + cc3
Let Da, Db and Dc be the fuzzy sets associated with the
terms ka, kb and kc, respectively
p. 128

Da
Db
cc cc
cc
D
= cc
+ cc
+ cc
q
1
2
3
Dc
Let µa,j , µb,j , and µc,j be the degrees of memberships of
document dj in the fuzzy sets Da, Db, and Dc. Then,
cc1
=
cc2
=
cc3 p. 129
µa,jµb,jµc,j
µa,jµb,j (1 − µc,j )
µa,j (1 − µb,j )(1 − µc,j
)

Da
Db
cc cc
cc
D = cc + cc
+ cc
q 1
2
3
Dc
µq,j
p. 130
=
µcc1+cc2+cc3,j
3
Y
i
cc ,j
= 1 − (1 − µ
) i=1
= 1 − (1 − µa,jµb,jµc,j ) ×
(1 − µa,jµb,j (1 − µc,j )) × (1 − µa,j (1 − µb,j )(1 −
µc,j ))

Conclusions
Fuzzy IR models have been discussed mainly in the
literature associated with fuzzy theory
They provide an interesting framework which naturally
embodies the notion of term dependencies
Experiments with standard test collections are not
available
p. 131

Alternative Algebraic Models
Generalized Vector Model
Neural Network Model
p. 132

p. 133

Classic models enforce independence of index terms
For instance, in the Vector model
A set of term vectors {→k1, →k2, . . ., →kt } are linearly
independent Frequently, this is interpreted as 6i ,j ⇒ →ki •
→kj = 0
In the generalized vector space model, two index term
vectors might be non-orthogonal
p. 134

Key Idea
As before, let wi,j be the weight associated with [ki, dj ]
and V = {k1, k2, . . ., kt} be the set of all terms
If the wi,j weights are binary, all patterns of occurrence
of terms within docs can be represented by minterms:
(k1, k2, k3, . . . , kt)
.
p. 135
m1 = (0, 0, 0, . . . , 0)
m2 = (1, 0, 0, . . . , 0)
m3 = (0, 1, 0, . . . , 0)
m4 = (1, 1, 0, . . . , 0)
m2t
.
= (1, 1, 1, . . . , 1)
For instance, m2 indi-
cates documents in which
solely the term k1 occurs

Key Idea
For any document dj , there is a minterm mr that
includes exactly the terms that occur in the document
Let us define the following set of minterm vectors m→
r,
1, 2, . . . , 2t
m→ 1 = (1, 0, .
. . , 0)
m→ 2 = (0, 1, .
. . , 0)
p. 136
.
.
= (0, 0, . . . ,
1)
m
→
2t
Notice that we can associate
each unit vector m→ r
with a minterm mr , and that
m→ i • m→ j = 0 for all i /= j

Key Idea
Pairwise orthogonality among the m→ r vectors does
not imply independence among the index terms
On the contrary, index terms are now correlated by
the
m→ r vectors
For instance, the vector m→ 4 is associated with the minterm
m4 = (1, 1, . . . , 0)
This minterm induces a dependency between terms k1 and k2
Thus, if such document exists in a collection, we say that the
minterm m4 is active
The model adopts the idea that co-occurrence of terms
induces dependencies among these terms
p. 137

Forming the Term Vectors
Let on(i, mr ) return the weight {0, 1} of the index term
ki
in the minterm mr
The vector associated with the term ki is computed as:
→
k
i =
Σ
∀r on(i, m ) c
m→
r i,r r
q Σ
∀r r
on(i, m )
c2
i,r
ci,r
=
Σ
dj | c(dj )=mr
wi,j
Notice that for a collection of size N , only N minterms
affect the ranking (and not 2t)
p. 138

Dependency between Index Terms
A degree of correlation between the terms ki and kj can
now be computed as:
→
→
i j
k • k
=
Σ
∀r
This degree of correlation sums up the dependencies
between ki and kj induced by the docs in the collection
on(i, mr ) × ci,r × on(j, mr ) ×
c
j,r
p. 139

The Generalized Vector Model
An Example
K1
K2
K3
d2
d4
d6
d5
d1
d7
d3
K1 K2 K3
d1 2 0 1
d2 1 0 0
d3 0 1 3
d4 2 0 0
d5 1 2 4
d6 1 2 0
d7 0 5 0
q 1 2 3
p. 140

Computation of ci,r
K1 K2 K3
d1
2 0 1
d2
1 0 0
d3
0 1 3
d4
2 0 0
d5
1 2 4
d6
0 2 2
d7
0 5 0
q 1 2 3
K1 K2 K3
d1 = m6
1 0 1
d2 = m2
1 0 0
d3 = m7
0 1 1
d4 = m2
1 0 0
d5 = m8
1 1 1
d6 = m7
0 1 1
d7 = m3
0 1 0
q = m8
1 1 1
c1,r c2,r c3,r
m1
0 0 0
m2
3 0 0
m3
0 5 0
m4
0 0 0
m5
0 0 0
m6
2 0 1
m7
0 3 5
m8
1 2 4
p. 141

Computation of
−→
ki
−
→
k
1 = 2 6 8
(3m→
+2m→ +m→
)
√
32+22+12
−
→
k
2 = 3 7 8
(5m→ +3m→
+2m→ )
√
5+3+2
−
→
k
3 = 6 7 8
(1m→ +5m→
+4m→ )
√
1+5+4
c1,r c2,r c3,r
m1
0 0 0
m2
3 0 0
m3
0 5 0
m4
0 0 0
m5
0 0 0
m6
2 0 1
m7
0 3 5
m8
1 2 4
p. 142

Computation of Document Vectors
−→
d1 =
2
−→
k1 +
−→
k3
−→
d2 =
−→
k1
−→
d3 =
−→
k2
+ 3
−→
k3
−→
d4 =
−→
d5 =
−→
k1
+
2
−→
k
2 +
4
−→
k
3
−→
d6 = 2
−→
k2 +
2
−→
k3
−→
d7 = 5
−→
k2
−→q =
−→
k1 +
2
→−
k2 + 3
→−
k3
K1 K2 K3
d1
2 0 1
d2
1 0 0
d3
0 1 3
d4
2 0 0
d5
1 2 4
d6
0 2 2
d7
0 5 0
q 1 2 3
p. 143

Conclusions
Model considers correlations among index terms
Not clear in which situations it is superior to the
standard Vector model
Computation costs are higher
Model does introduce interesting new ideas
p. 144

p. 145

Classic IR might lead to poor retrieval due to:
unrelated documents might be included in the
answer set
relevant documents that do not contain at least one
index term are not retrieved
Reasoning: retrieval based on index terms is vague
and noisy
The user information need is more related to concepts
and ideas than to index terms
A document that shares concepts with another
document known to be relevant might be of interest
p. 146

The idea here is to map documents and queries into a
dimensional space composed of concepts
Let
t: total number of index terms
N : number of documents
M = [mi j ]: term-document matrix t × N
To each element of M is assigned a weight wi,j
associated with the term-document pair [ki, dj ]
The weight wi , j can be based on a tf-idf weighting scheme
p. 147

The matrix M = [mi j ] can be decomposed into
three components using singular value
decomposition
M = K · S · DT
were
K is the matrix of eigenvectors derived from C = M ·
MT
D T is the matrix of eigenvectors derived from MT · M
S is an r × r diagonal matrix of singular values where
r = min(t, N ) is the rank of M
p. 148

Computing an Example
Let MT = [mi j ] be given
by
K1 K2 K3 q • dj
d1
2 0 1 5
d2
1 0 0 1
d3
0 1 3 11
d4
2 0 0 2
d5
1 2 4 17
d6
1 2 0 5
d7
0 5 0 10
q 1 2 3
Compute the matrices K, S, and Dt
p. 149

In the matrix S, consider that only the s largest singular
values are selected
Keep the corresponding columns in K and DT
The resultant matrix is called Ms and is given by
s s s
M = K · S · DT
s
where s, s < r, is the dimensionality of a reduced
concept space
The parameter s should be
large enough to allow fitting the characteristics of the
data
small enough to filter out the non-relevant
representational details
p. 150

Latent Ranking
The relationship between any two documents in s can
be obtained from the MT · Ms matrix given by
M T
s · Ms = (Ks s s
· S · D
)
T T
s s
· K · S · DT
s
s s
T
s s s
= D · S · K · K · S · DT
s
s s s
= D · S · S · DT
s
T
= (Ds · Ss) · (Ds · Ss)
In the above matrix, the (i, j) element quantifies
the relationship between documents di and dj
p. 151

Latent Ranking
The user query can be modelled as a
pseudo-document in the original M matrix
Assume the query is modelled as the document
numbered 0 in the M matrix
s
The matrix MT · Ms quantifies the relationship between
any two documents in the reduced concept space
The first row of this matrix provides the rank of all the
documents with regard to the user query
p. 152

Conclusions
Latent semantic indexing provides an interesting
conceptualization of the IR problem
Thus, it has its value as a new theoretical
framework
From a practical point of view, the latent semantic
indexing model has not yielded encouraging results
p. 153

Classic IR:
Terms are used to index documents and queries
Retrieval is based on index term matching
Motivation:
Neural networks are known to be good pattern
matchers
p. 155

The human brain is composed of billions of neurons
Each neuron can be viewed as a small processing unit
A neuron is stimulated by input signals and emits output
signals in reaction
A chain reaction of propagating signals is called a
spread activation process
As a result of spread activation, the brain might
command the body to take physical reactions
p. 156

A neural network is an oversimplified representation of
the neuron interconnections in the human brain:
nodes are processing units
edges are synaptic connections
the strength of a propagating signal is modelled by a
weight assigned to each edge
the state of a node is defined by its activation level
depending on its activation level, a node might issue
an output signal
p. 157

A neural network model for information retrieval
p. 158

Three layers network: one for the query terms, one for
the document terms, and a third one for the documents
Signals propagate across the network
First level of propagation:
Query terms issue the first signals
These signals propagate across the network to
reach the document nodes
Second level of propagation:
Document nodes might themselves generate new
signals which affect the document term nodes
Document term nodes might respond with new
signals of their own
p. 159

Quantifying Signal Propagation
Normalize signal strength (MAX = 1)
Query terms emit initial signal equal to 1
Weight associated with an edge from a query term
node ki to a document term node ki:
i,q wi,q
w = q Σ t
i=1
2
wi,q
Weight associated with an edge from a document term
node ki to a document node dj :
i,j
w
=
wi,j
q Σ
p. 160
t 2
i = 1 wi,j

Quantifying Signal Propagation
After the first level of signal propagation, the activation
level of a document node dj is given by:
t
Σ
i=1
i,q i,j
w w
=
Σ t
i=1 wi,q wi,j
q Σ t
i=1 w2
i,q ×
q Σ t
i=1
2
wi,j
which is exactly the ranking of the Vector model
New signals might be exchanged among document
term nodes and document nodes
A minimum threshold should be enforced to avoid
spurious signal generation
p. 161

Conclusions
Model provides an interesting formulation of the IR
problem
Model has not been tested extensively
It is not clear the improvements that the model might
provide
p. 162

Chapter 3
Modeling
Part III: Alternative Probabilistic
Models
BM25
Language Models
Divergence from Randomness
Belief Network Models
Other Models
p. 163

BM25 (Best Match 25)
BM25 was created as the result of a series of
experiments on variations of the probabilistic model
A good term weighting is based on three principles
inverse document frequency
term frequency
document length
normalization
The classic probabilistic model covers only the first of
these principles
This reasoning led to a series of experiments with the
Okapi system, which led to the BM25 ranking formula
p. 165

BM1, BM11 and BM15 Formulas
At first, the Okapi system used the Equation below as
ranking formula
sim(dj , q)
~
Σ
ki∈q∧ki∈dj
N − ni +
0.5
log ni +
0.5
which is the equation used in the probabilistic model,
when no relevance information is provided
It was referred to as the BM1 formula (Best Match 1)
p. 166

The first idea for improving the ranking was to introduce
a term-frequency factor Fi , j in the BM1 formula
This factor, after some changes, evolved to become
F i,j = S1
× f i,j
K 1 + f i,j
where
fi , j is the frequency of term ki within document dj
K1 is a constant setup experimentally for each collection
S1 is a scaling constant, normally set to S1 = (K1 + 1)
If K1 = 0, this whole factor becomes equal to 1
and bears no effect in the ranking
p. 167

The next step was to modify the Fi , j factor by adding
document length normalization to it, as follows:
'
Fi , j = S1 × f i,j
×
1 j
K len(d )
avg_doclen + f i,j
where
len(dj ) is the length of document dj (computed, for instance,
as the number of terms in the document)
avg_doclen is the average document length for the collection
p. 168

Next, a correction factor Gj,q dependent on the
document and query lengths was added
Gj,q = K2
avg_doclen −
len(dj )
× len(q) × avg_doclen +
len(dj )
where
len(q) is the query length (number of terms in the query)
K2 is a constant
p. 169

A third additional factor, aimed at taking into account
term frequencies within queries, was defined as
Fi,q = S3
× fi,q
K3 + fi,q
where
fi , q is the frequency of term ki within query
q K3 is a constant
S3 is an scaling constant related to K3 ,
normally set to
S3 = (K3 + 1)
p. 170

Introduction of these three factors led to various BM
(Best Matching) formulas, as follows:
B M 1 j
sim (d , q) ~
Σ
ki [q,dj ]
lo
g
i
N − n +
0.5
ni +
0.5
simB M 15 j j,q
(d , q) ~ G
+
Σ
k i [q,dj ]
F i,j i,q
× F ×
lo
g
i
N − n +
0.5
ni +
0.5
simB M 11 j j,q
(d , q) ~ G
+
Σ
k i [q,dj ]
F
'
i,j i,q
× F
×
lo
g
i
N − n +
0.5
ni +
0.5
p. 171
where ki[q, dj ] is a short notation for ki ∈ q Λ ki ∈
dj

Experiments using TREC data have shown that BM11
outperforms BM15
Further, empirical considerations can be used to
simplify the previous equations, as follows:
Empirical evidence suggests that a best value of K2 is 0,
which eliminates the Gj,q factor from these equations
Further, good estimates for the scaling constants S1 and S3
are K1 + 1 and K3 + 1, respectively
Empirical evidence also suggests that making K3 very large
is better. As a result, the Fi,q factor is reduced simply to fi,q
For short queries, we can assume that fi,q is 1 for all terms
p. 172

These considerations lead to simpler equations as
follows
B M 1 j
sim (d , q) ~
Σ
k i [q,dj ]
lo
g
i
N − n +
0.5
ni +
0.5
simB M 15 j
(d , q) ~
Σ
k i [q,dj ]
(K1 + 1)fi , j
(K1 +
fi , j )
× lo
g
i
N − n +
0.5 i
n +
0.5
simB M 11 j
(d , q) ~
Σ
k i [q,dj ]
(K1 + 1)fi , j
K 1 len(dj )
avg_doclen + fi,j
× lo
g
i
N − n +
0.5
ni +
0.5
p. 173

BM25 Ranking Formula
BM25: combination of the BM11 and BM15
The motivation was to combine the BM11 and BM25
term frequency factors as follows
Bi,j =
(K1 +
1)fi,j
K1
h
len(dj )
(1 − b) + bavg_doclen
i
+ f i,j
where b is a constant with values in the interval [0,
1]
If b = 0, it reduces to the BM15 term frequency
factor If b = 1, it reduces to the BM11 term
frequency factor
For values of b between 0 and 1, the equation provides a
combination of BM11 with BM15
p. 174

The ranking equation for the BM25 model can then be
written as
Σ
simB M 25(dj, q) ~
B ki[q,dj ]
i,j × lo
g
i
N − n +
0.5
ni +
0.5
where K1 and b are empirical constants
K1 = 1 works well with real collections
b should be kept closer to 1 to emphasize the document length
normalization effect present in the BM11 formula
For instance, b = 0.75 is a reasonable assumption
Constants values can be fine tunned for particular collections
through proper experimentation
p. 175

Unlike the probabilistic model, the BM25 formula can be
computed without relevance information
There is consensus that BM25 outperforms the classic
vector model for general collections
Thus, it has been used as a baseline for evaluating new
ranking functions, in substitution to the classic vector
model
p. 176

Language Models
Language models are used in many natural language
processing applications
Ex: part-of-speech tagging, speech recognition, machine
translation, and information retrieval
To illustrate, the regularities in spoken language can be
modeled by probability distributions
These distributions can be used to predict the likelihood
that the next token in the sequence is a given word
These probability distributions are called language
models
p. 178

Language Models
A language model for IR is composed of the following
components
A set of document language models, one per document dj of the
collection
A probability distribution function that allows estimating the
likelihood that a document language model Mj generates each
of the query terms
A ranking function that combines these generating probabilities
for the query terms into a rank of document dj with regard to the
query
p. 179

Statistical Foundation
Let S be a sequence of r consecutive terms that occur
in a document of the collection:
S = k1 , k2, . . . , kr
An n-gram language model uses a Markov process to
assign a probability of occurrence to S:
r
Y
Pn(S) = P (k
| i=1
where n is the order of the Markov process
The occurrence of a term depends on observing the
n − 1 terms that precede it in the text
i i−1 i−2 i−(n−1)
k , k , . . . , k
)
p. 180

Statistical Foundation
Unigram language model (n = 1): the estimatives
are based on the occurrence of individual words
Bigram language model (n = 2): the estimatives
are based on the co-occurrence of pairs of words
Higher order models such as Trigram language
models (n = 3) are usually adopted for speech
recognition
Term independence assumption: in the case of IR,
the impact of word order is less clear
As a result, Unigram models have been used extensively in IR
p. 181

Multinomial Process
Ranking in a language model is provided by estimating
P (q|Mj )
Several researchs have proposed the adoption of a
multinomial process to generate the query
According to this process, if we assume that the query
terms are independent among themselves (unigram
model), we can write:
Y
P (q|M ) = P (k
|
p. 182
j i j
ki∈q
M )

Multinomial Process
By taking logs on both sides
Σ
ki∈q
i
log P (q|Mj ) = log P
(k |
j
M )
Σ
= log P∈ (ki |Mj )
+ ki∈qΛdj
Σ
ki ∈qΛчdj
log P/∈(ki|
Mj )
=
Σ
lo
g
∈ i j
P (k |
M )
/∈ i j
P (k |
M )
ki∈qΛdj
ki∈q
Σ
/∈ i j
+ log P(k |
M )
where P∈ and P/∈ are two distinct probability
distributions:
The first is a distribution for the query terms in the document
The second is a distribution for the query terms not in the
document
p. 183

Multinomial Process
For the second distribution, statistics are derived from
all the document collection
Thus, we can write
P/∈(ki|Mj ) = αj P (ki|C)
where αj is a parameter associated with document dj
and P (ki|C) is a collection C language model
p. 184

Multinomial Process
P (ki|C) can be estimated in different ways
For instance, Hiemstra suggests an idf-like estimative:
P (ki|C)
=
ni
Σ
i ni
where ni is the number of docs in which ki occurs
Miller, Leek, and Schwartz suggest
P (ki|C)
=
Fi
Σ
p. 185
i Fi
where Fi =
Σ
j
fi , j

Multinomial Process
Thus, we obtain
j
log P (q|M )
=
Σ
k i ∈q∧dj
lo
g
P∈(ki|Mj )
αj P (ki|C)
q j
+ n log α
+
Σ
k i ∈q
i
log P (k |
C)
~
Σ
k i ∈q∧dj
lo
g
P∈(ki|Mj )
αj P (ki|C)
p. 186
q
+ n log
α
j
where nq stands for the query length and the last sum
was dropped because it is constant for all documents

Multinomial Process
The ranking function is now composed of two separate
parts
The first part assigns weights to each query term that
appears in the document, according to the expression
lo
g
∈ i j
P (k |
M )
αj P (ki|
C)
This term weight plays a role analogous to the tf plus idf
weight components in the vector model
Further, the parameter αj can be used for document
length normalization
p. 187

Multinomial Process
The second part assigns a fraction of probability mass
to the query terms that are not in the document—a
process called smoothing
The combination of a multinomial process with
smoothing leads to a ranking formula that naturally
includes tf , idf , and document length
normalization
That is, smoothing plays a key role in modern language
modeling, as we now discuss
p. 188

Smoothing
In our discussion, we estimated P/∈(ki|Mj ) using P (ki|
C) to avoid assigning zero probability to query terms not
in document dj
This process, called smoothing, allows fine tuning the
ranking to improve the results.
One popular smoothing technique is to move some
mass probability from the terms in the document to the
terms not in the document, as follows:
P (ki|Mj )
=
p. 189
(
s
∈
P (k
|
i j
αj P (ki|
C)
M ) if ki ∈ dj
otherwi
se
where Ps (ki |Mj ) is the smoothed distribution
for terms in
∈
document dj

Smoothing
Under the above assumptions, the smoothing
j
s
∈
parameter α is also a function of P (k
|
i j
M )
As a result, distinct smoothing methods can be
s
∈
obtained through distinct specifications of P (k
|
i j
M )
Examples of smoothing methods:
Jelinek-Mercer Method
Bayesian Smoothing using Dirichlet Priors
p. 191

Jelinek-Mercer Method
The idea is to do a linear interpolation between the
document frequency and the collection frequency
distributions:
s
∈
P (k
|
i j
M , λ) = (1 −
λ)
f i,j
Σ
i f i,j
+ λ
Fi
Σ
i Fi
where 0 ≤ λ ≤ 1
It can be shown that
αj = λ
Thus, the larger the values of λ, the larger is the effect
of smoothing
p. 192

Dirichlet smoothing
In this method, the language model is a multinomial
distribution in which the conjugate prior probabilities are
given by the Dirichlet distribution
This leads to
s
P∈(ki|Mj, λ) =
i,j
f + λ Fi
Σ
i Fi
Σ
i i,j
f + λ
As before, closer is λ to 0, higher is the influence of the
term document frequency. As λ moves towards 1, the
influence of the term collection frequency increases
p. 193

Dirichlet smoothing
Contrary to the Jelinek-Mercer method, this influence is
always partially mixed with the document frequency
It can be shown that
j
α
=
λ
Σ
i i,j
f + λ
As before, the larger the values of λ, the larger is the
effect of smoothing
p. 194

Smoothing Computation
In both smoothing methods above, computation can be
carried out efficiently
All frequency counts can be obtained directly from the
index
The values of αj can be precomputed for each
document
Thus, the complexity is analogous to the computation of
a vector space ranking using tf-idf weights
p. 195

Applying Smoothing to Ranking
The IR ranking in a multinomial language model is
computed as follows:
s
∈
compute P (k
|
i j
M ) using a smoothing method
i
compute P (k |C)
using
Σ
n
or
ni Fi
Σ
i i F
i i
compute αj from the Equation αj = 1 −
Σ
ki ∈dj
∈
P s (ki |
Mj )
1
−
Σ
k ∈d
i j
P (ki |C)
compute the ranking using the formula
p. 196
Σ
log P (q|Mj ) =
log ki∈qΛdj
s
P (k
|
i j
M )
∈
αj P (ki|
C)
+ nq log
αj

Bernoulli Process
j i j
P (q|M ) = P (k |
M ) ki∈q
ki/∈q
where P (ki|Mj ) are term probabilities
This is analogous to the expression for ranking
computation in the classic probabilistic model
×
The first application of languages models to IR was due
to Ponte & Croft. They proposed a Bernoulli process for
generating the query, as we now discuss
Given a document dj , let Mj be a reference to
a language model for that document
If we assume independence of index terms, we can
compute P (q|Mj ) using a multivariate Bernoulli
process:
Y Y [1 − P (ki|
Mj )]
p. 197

Bernoulli process
A simple estimate of the term probabilities is
P (ki|Mj )
=
f i,j
Σ
l f l,j
which computes the probability that term ki will be
produced by a random draw (taken from dj )
However, the probability will become zero if ki does not
occur in the document
Thus, we assume that a non-occurring term is related to
dj with the probability P (ki|C) of observing ki in the
whole collection C
p. 198

Bernoulli process
P (ki|C) can be estimated in different ways
For instance, Hiemstra suggests an idf-like estimative:
P (ki|C)
=
ni
Σ
l nl
where ni is the number of docs in which ki occurs
Miller, Leek, and Schwartz suggest
P (ki|C)
=
Fi
Σ
l Fl
i
Σ
where F = f
j
i,j
This last equation for P (ki|C) is adopted here
p. 199

Bernoulli process
As a result, we redefine P (ki|Mj ) as
follows:
,
P (ki|Mj )
=
,

,
f i,j
Σ
i f i , j
if fi , j >
0
Fi
, Σ i Fi
if fi , j =
0
In this expression, P (ki|Mj ) estimation is based only
on
the document dj when fi , j > 0
This is clearly undesirable because it leads to instability
in the model
p. 200

Bernoulli process
This drawback can be accomplished through an
average computation as follows
i
P (k )
=
Σ
i
j|k ∈dj
P (ki|
Mj )
ni
That is, P (ki) is an estimate based on the
language models of all documents that contain
term ki
However, it is the same for all documents that contain
term ki
That is, using P (ki) to predict the generation of term
ki
by the Mj involves a risk
p. 201

Bernoulli process
i,j
p. 202
i
f = P
(k )
×
To fix this, let us define the average frequency fi , j
of term ki in document dj as
Σ
i
f i,j

Bernoulli process
The risk Ri , j associated with using fi , j can
be quantified by a geometric distribution:
Ri,j =
1 ×
f i,j
! !
1 + f 1 +
f
i,j i,j
f i,j
For terms that occur very frequently in the collection,
fi , j 0 and Ri , j ~ 0
For terms that are rare both in the document and in the
collection, fi , j ~ 1, fi , j ~ 1, and Ri , j ~ 0.25
p. 203

Bernoulli process
Let us refer the probability of observing term ki
according to the language model Mj as PR (ki |Mj )
We then use the risk factor Ri , j to compute PR (ki |
Mj ), as follows
PR (ki |Mj )
=
,
, P (ki|Mj )(1−Ri , j ) × P (ki)Ri,j
,
, F
if fi , j >
0
i
Σ
i Fi
otherwi
se
In this formulation, if Ri , j ~ 0 then PR (ki |Mj ) is
basically
a function of P (ki|Mj )
Otherwise, it is a mix of P (ki) and P (ki|
Mj )
p. 204

Bernoulli process
j R i j
P (q|M ) = P (k |
M ) ki∈q ki/∈q
which computes the probability of generating the query
from the language (document) model
This is the basic formula for ranking computation in a
language model based on a Bernoulli process for
generating the query
×
Substituting into original P (q|Mj ) Equation, we obtain
Y Y
[1 − PR (ki |
Mj )]
p. 205

p. 206

A distinct probabilistic model has been proposed by
Amati and Rijsbergen
The idea is to compute term weights by measuring the
divergence between a term distribution produced by a
random process and the actual term distribution
Thus, the name divergence from randomness
The model is based on two fundamental assumptions,
as follows
p. 207

First assumption:
Not all words are equally important for describing the content of
the documents
Words that carry little information are assumed to be randomly
distributed over the whole document collection C
Given a term ki , its probability distribution over the whole
collection is referred to as P (ki|C)
The amount of information associated with this distribution is
given by
— log P (ki|C)
By modifying this probability function, we can implement
distinct
notions of term randomness
p. 208

Second assumption:
A complementary term distribution can be obtained by
considering just the subset of documents that contain term ki
This subset is referred to as the elite set
The corresponding probability distribution, computed with regard
to document dj , is referred to as P (ki|dj )
Smaller the probability of observing a term ki in a document
dj , more rare and important is the term considered to be
Thus, the amount of information associated with the term in the
elite set is defined as
1 − P (ki|dj )
p. 209

Given these assumptions, the weight wi,j of a term ki in
a document dj is defined as
wi,j = [− log P (ki|C)] × [1 − P (ki|dj )]
Two term distributions are considered: in the collection
and in the subset of docs in which it occurs
The rank R(dj , q) of a document dj with regard to
a query q is then computed as
R(dj , q) =
Σ
k i ∈ q fi,q × wi,j
where fi, q is the frequency of term ki in the query
p. 210

Random Distribution
To compute the distribution of terms in the collection,
distinct probability models can be considered
For instance, consider that Bernoulli trials are used to
model the occurrences of a term in the collection
To illustrate, consider a collection with 1,000 documents
and a term ki that occurs 10 times in the collection
Then, the probability of observing 4 occurrences of
term ki in a document is given by
P (ki|C)
=
p. 211
10 1 1
1 −
4 1000
1000
4
6
which is a standard binomial distribution

Random Distribution
In general, let p = 1/N be the probability of observing
a term in a document, where N is the number of docs
The probability of observing fi , j occurrences of term ki
in document dj is described by a binomial distribution:
Fi
f i,j
P (ki|C) =
p
f i ,j
F i − f i , j
× (1 − p)
Define
p. 212
λi = p
×
Fi
and assume that p → 0 when N → ∞, but that

Random Distribution
Under these conditions, we can aproximate the
binomial distribution by a Poisson process, which yields
P (ki|C)
=
e−λi λ fi ,j
i
f i,j
!
p. 213

Random Distribution
— log P (ki|C) = −
log
−λ i
e λ i
f ,j
i
i,j
f
!
The amount of information associated with term ki in
the collection can then be computed as
!
≈ −fi , j log λi + λi log e +
log(fi , j !)
i,j
≈ f
log
i,j
i
+ λ
+
f 1
λi 12fi , j +
1
i,j
— f log
e
1
+
log(2πfi,j )
2
in which the logarithms are in base 2 and the factorial
term fi , j ! was approximated by the Stirling’s
formula i,j
√
f ! ≈ 2π f
p. 214
i,j
(f +0.5)
i,j e i ,j
−1
−f e(12fi , j +1)

Random Distribution
Another approach is to use a Bose-Einstein distribution
and approximate it by a geometric distribution:
P (ki|C) ≈ p × pf i , j
where p = 1/(1 + λi )
The amount of information associated with term ki in
the collection can then be computed as
— log P (ki|C) ≈ −
log
i,j ×
— f
log
λi
1
1 + λi 1
+ λi
p. 215
which provides a second form of computing the term
distribution over the whole collection

Distribution over the Elite Set
The amount of information associated with term
distribution in elite docs can be computed by using
Laplace’s law of succession
1
1 − P (ki|dj ) =
f i , j +
1
Another possibility is to adopt the ratio of two Bernoulli
processes, which yields
1 − P (ki|dj )
=
Fi +
1
ni × (fi , j +
1)
p. 216
where ni is the number of documents in which the term
occurs, as before

Normalization
These formulations do not take into account the length
of the document dj . This can be done by normalizing
the term frequency fi , j
Distinct normalizations can be used, such as
f
'
i,j = f i,j
avg_doclen
×
len(dj
)
p. 217
or
f
'
i,j i,j ×
= f log 1
+
avg_doclen
len(dj )
where avg_doclen is the average document length in the
collection and len(dj ) is the length of document dj

Normalization
To compute wi,j weights using normalized term
frequencies, just substitute the factor fi , j by fi
'
,j
In here we consider that a same normalization is
applied for computing P (ki|C) and P (ki|dj )
By combining different forms of computing P (ki|C)
and P (ki|dj ) with different normalizations, various
ranking formulas can be produced
p. 218

Bayesian Network Models
p. 219

Bayesian Inference
One approach for developing probabilistic models of IR
is to use Bayesian belief networks
Belief networks provide a clean formalism for combining
distinct sources of evidence
Types of evidences: past queries, past feedback cycles, distinct
query formulations, etc.
In here we discuss two models:
Inference network, proposed by Turtle and Croft
Belief network model, proposed by Ribeiro-Neto and Muntz
Before proceeding, we briefly introduce Bayesian
networks
p. 220

Bayesian Networks
Bayesian networks are directed acyclic graphs
(DAGs) in which
the nodes represent random variables
the arcs portray causal relationships between these
variables
the strengths of these causal influences are expressed by
conditional probabilities
The parents of a node are those judged to be direct
causes for it
This causal relationship is represented by a link
directed from each parent node to the child node
The roots of the network are the nodes without
parents
p. 221

Bayesian Networks
Let
xi be a node in a Bayesian network G
Γx i
be the set of parent nodes of xi
The influence of Γxi on xi can be specified by any set
of functions Fi(xi, Γxi ) that satisfy
Σ
∀xi
p. 222
i i xi
F (x , Γ ) =
1
0 ≤ Fi(xi, Γxi ) ≤
1
where xi also refers to the states of the random variable
associated to the node xi

Bayesian Networks
A Bayesian network for a joint probability distribution
P (x1, x2, x3, x4, x5)
p. 223

Bayesian Networks
The dependencies declared in the network allow the
natural expression of the joint probability distribution
P (x1, x2 , x3 , x4 , x5) = P (x1)P (x2|x1)P (x3|x1)P (x4|x2, x3)P
(x5|x3)
The probability P (x1) is
called the prior probability
for the network
It can be used to model previ-
ous knowledge about the se-
mantics of the application
p. 224

Inference Network Model
p. 225

An epistemological view of the information retrieval
problem
Random variables associated with documents, index
terms and queries
A random variable associated with a document dj
represents the event of observing that document
The observation of dj asserts a belief upon the random
variables associated with its index terms
p. 226

An inference network for information retrieval
Nodes of the network
documents (dj )
index terms (ki)
queries (q, q1, and q2)
user information need (I)
p. 227

The edges from dj to the nodes ki indicate that the
observation of dj increase the belief in the variables ki
dj has index terms k2, ki, and kt
q has index terms k1, k2, and ki
q1 and q2 model boolean
formulation
q1 = (k1 Λ k2) V
ki) I = (q V q1)
p. 228

Let →k = (k1, k2, . . . , kt) a t-dimensional
vector ki ∈ {0, 1}, then k has 2t possible
states Define
→
on(i, k)
=
(
1 if ki = 1 according
to →k
0 otherwise
Let dj ∈ {0, 1} and q ∈ {0, 1}
The ranking of dj is a measure of how much evidential
support the observation of dj provides to the query
p. 229

The ranking is computed as P (q Λ dj ) where q and dj
are short representations for q = 1 and dj = 1,
respectively
dj stands for a state where dj = 1 and 6l/=j ⇒ dl =
0, because we observe one document at a time
Σ
P (q Λ dj ) = P
(q ∀
→k
j
Λ d |k) ×
→
→
P
(k)
Σ
= P
(q ∀
→k
j
→
Λ d Λ
k)
Σ
= P (q|
d ∀
→k
j
→ ×
j
→
Λ k) P (d Λ
k)
Σ
→
→
× ×
j j
= P (q|k) P (k|d ) P
(d )
∀→k
P (q Λ dj ) = 1 − P (q Λ dj
)
p. 230

Prior Probabilities
The prior probability P (dj ) reflects the probability
of observing a given document dj
In Turtle and Croft this probability is set to 1/N ,
where
N is the total number of documents in the system:
1
1
P (dj ) =
N
P (dj ) = 1 −
N
To include document length normalization in the model,
we could also write P (dj ) as follows:
j
P (d )
=
1
→
j
|d |
P (dj ) = 1 − P
(dj )
p. 232
where |d→j | stands for the norm of the vector
d→j

Network for Boolean Model
How an inference network can be tuned to subsume the
Boolean model?
First, for the Boolean model, the prior probabilities are
given by:
1
1 P (dj ) =
N
P (dj ) = 1 −
N
Regarding the conditional probabilities P (ki|dj ) and
P (q|→k), the specification is as follows
(
1 if ki ∈ dj
0
otherwise
P (ki|dj )
=
P (ki|dj )
=
p. 233
1 − P (ki|
dj )

Network for Boolean Model
We can use P (ki|dj ) and P (q|→k) factors to compute
the evidential support the index terms provide to q:
(
1 if c(q) =
c(→k)
0 otherwise
P (q|→k)=
P (q|→k)= 1 − P (q|
→k)
where c(q) and c(→k) are the conjunctive
components associated with q and →k, respectively
By using these definitions in P (q Λ dj ) and P (q Λ dj
)
equations, we obtain the Boolean form of retrieval
p. 234

Network for TF-IDF Strategies
For a tf-idf ranking strategy
Prior probability P (dj ) reflects the importance
of
document normalization
j
P (d )
=
1
→
j
|d |
P (dj ) = 1 − P
(dj )
p. 235

For the document-term beliefs, we write:
P (ki|dj ) = α + (1 − α) × fi , j
× idf i
P (ki|dj ) = 1 − P (ki|dj )
where α varies from 0 to 1, and empirical
evidence suggests that α = 0.4 is a good default
value
Normalized term frequency and inverse document
frequency:
f i , j =
f i,j
maxi fi , j
log
N
p. 236
idf i = n i
log
N

For the term-query beliefs, we write:
Σ
ki∈q
i,j
× wq
P (q|→k)= f
P (q|→k)= 1 − P (q|
→k)
p. 237
where wq is a parameter used to set the maximum
belief achievable at the query node

By substituting these definitions into P (q Λ dj ) and
P (q Λ dj ) equations, we obtain a tf-idf form of ranking
We notice that the ranking computed by the inference
network is distinct from that for the vector model
However, an inference network is able to provide good
retrieval performance with general collections
p. 238

Combining Evidential Sources
In Figure below, the node q is the standard
keyword-based query formulation for I
The second query q1 is a Boolean-like query formulation
for the same information need
p. 239

Combining Evidential Sources
Let I = q V q1
In this case, the ranking provided by the inference
network is computed as
P (I Λ dj )
=
Σ
→
k
→
P (I|
k)
× →
P
(k|
j × j
d ) P
(d )
=
Σ
→k
which might yield a retrieval performance which
surpasses that of the query nodes in isolation (
Turtle and Croft)
1
p. 240
→
→
(1 − P (q|k) P (q
|k))
× → j
P (k|d
)
× j
P
(d )

Belief Network Model
The belief network model is a variant of the inference
network model with a slightly different network topology
As the Inference Network Model
Epistemological view of the IR problem
Random variables associated with documents, index
terms and queries
Contrary to the Inference Network Model
Clearly defined sample space
Set-theoretic view
p. 242

By applying Bayes’ rule, we can write
p. 243
P (dj |q) = P (dj Λ q)/P
(q)
P (dj |q) ~
Σ
∀→k
because P (q) is a constant for all documents in the
collection
j ×
→
→
P (d Λ q|k) P
(k)

Instantiation of the index term variables separates the
nodes q and d making them mutually independent:
Σ
∀→k
To complete the belief network we need to specify the
conditional probabilities P (q|→k) and P (dj |→k)
Distinct specifications of these probabilities allow the
modeling of different ranking strategies
j
P (dj |q) ~ P (d |
k)
×
→
→
P (q|
k)
× →
P
(k)
p. 244

For the vector model, for instance, we define a vector
→ki given by
→ki = →k| on(i, →k) = 1 Λ 6j /=i on(i,
→k) = 0
The motivation is that tf-idf ranking strategies sum up
the individual contributions of index terms
We proceed as follows
→
,
wi,q
,
 q Σ
w2
t
i=1 i,q
if →k = →ki Λ
on(i, →q) = 1
otherwise
0
P (q|k)
=
P (q|→k)
p. 245
= 1 − P (q|
→k)

Further, define
j
P (d
|
→
k)
=
,
wi,j
,
 q
Σ
w2
t
i=1 i , j
if →k = →ki Λ
on(i, d→j ) = 1
otherwise
0
P (dj |→k) = 1 − P (dj |→k)
Then, the ranking of the retrieved documents coincides
with the ranking ordering generated by the vector model
p. 246

Computational Costs
In the inference network model only the states which
have a single document active node are considered
Thus, the cost of computing the ranking is linear on the
number of documents in the collection
However, the ranking computation is restricted to the
documents which have terms in common with the query
The networks do not impose additional costs because
the networks do not include cycles
p. 247

Other Models
Hypertext Model
Web-based Models
Structured Text
Retrieval
Multimedia Retrieval
Enterprise and Vertical Search
p. 248

The Hypertext Model
Hypertexts provided the basis for the design of the
hypertext markup language (HTML)
Written text is usually conceived to be read
sequentially
Sometimes, however, we are looking for information that
cannot be easily captured through sequential reading
For instance, while glancing at a book about the history of the
wars, we might be interested in wars in Europe
In such a situation, a different organization of the text is
desired
p. 250

The Hypertext Model
The solution is to define a new organizational structure
besides the one already in existence
One way to accomplish this is through hypertexts, that
are high level interactive navigational structures
A hypertext consists basically of nodes that are
correlated by directed links in a graph structure
p. 251

The Hypertext Model
Two nodes A and B might be connected by a directed
link lA B which correlates the texts of these two nodes
In this case, the reader might move to the node B while
reading the text associated with node A
When the hypertext is large, the user might lose track of
the organizational structure of the hypertext
To avoid this problem, it is desirable that the hypertext
include a hypertext map
In its simplest form, this map is a directed graph which displays
the current node being visited
p. 252

The Hypertext Model
Definition of the structure of the hypertext should be
accomplished in a domain modeling phase
After the modeling of the domain, a user interface
design should be concluded prior to implementation
Only then, can we say that we have a proper hypertext
structure for the application at hand
p. 253

Web-based Models
The first Web search engines were fundamentally IR
engines based on the models we have discussed here
The key differences were:
the collections were composed of Web pages (not documents)
the pages had to be crawled
the collections were much larger
This third difference also meant that each query word
retrieved too many documents
As a result, results produced by these engines were
frequently dissatisfying
p. 255

Web-based Models
A key piece of innovation was missing—the use of link
information present in Web pages to modify the ranking
There are two fundamental approaches to do this
namely, PageRank and Hubs-Authorities
Such approaches are covered in Chapter 11 of the book (Web
Retrieval)
p. 256

Structured Text Retrieval
p. 257

Structured Text Retrieval
All the IR models discussed here treat the text as a
string with no particular structure
However, information on the structure might be
important to the user for particular searches
Ex: retrieve a book that contains a figure of the Eiffel tower in a
section whose title contains the term “France”
The solution to this problem is to take advantage of the
text structure of the documents to improve retrieval
Structured text retrieval are discussed in Chapter 13 of
the book
p. 258

Multimedia Retrieval
Multimedia data, in the form of images, audio, and
video, frequently lack text associated with them
The retrieval strategies that have to be applied are quite
distinct from text retrieval strategies
However, multimedia data are an integral part of the
Web
Multimedia retrieval methods are discussed in great
detail in Chapter 14 of the book
p. 260

p. 261

Enterprise search is the task of searching for
information of interest in corporate document collections
Many issues not present in the Web, such as privacy,
ownership, permissions, are important in enterprise
search
In Chapter 15 of the book we discuss in detail some
enterprise search solutions
p. 262

A vertical collection is a repository of documents
specialized in a given domain of knowledge
To illustrate, Lexis-Nexis offers full-text search focused on the
area of business and in the area of legal
Vertical collections present specific challenges with
regard to search and retrieval
p. 263

Chapter 4
Retrieval Evaluation
The Cranfield Paradigm
Retrieval Performance Evaluation
Evaluation Using Reference Collections
Interactive Systems Evaluation
Search Log Analysis using
Clickthrough Data
p. 1

Introduction
To evaluate an IR system is to measure how well the
system meets the information needs of the users
This is troublesome, given that a same result set might be
interpreted differently by distinct users
To deal with this problem, some metrics have been defined that,
on average, have a correlation with the preferences of a group of
users
Without proper retrieval evaluation, one cannot
determine how well the IR system is performing
compare the performance of the IR system with that of other
systems, objectively
Retrieval evaluation is a critical and integral
component of any modern IR system
p. 2

Introduction
Systematic evaluation of the IR system allows
answering questions such as:
a modification to the ranking function is proposed, should we go
ahead and launch it?
a new probabilistic ranking function has just been devised, is it
superior to the vector model and BM25 rankings?
for which types of queries, such as business, product, and
geographic queries, a given ranking modification works best?
Lack of evaluation prevents answering these questions
and precludes fine tunning of the ranking function
p. 3

Introduction
Retrieval performance evaluation consists of
associating a quantitative metric to the results produced
by an IR system
This metric should be directly associated with the relevance of
the results to the user
Usually, its computation requires comparing the results produced
by the system with results suggested by humans for a same set
of queries
p. 4

Evaluation of IR systems is the result of early
experimentation initiated in the 50’s by Cyril Cleverdon
The insights derived from these experiments provide a
foundation for the evaluation of IR systems
Back in 1952, Cleverdon took notice of a new indexing
system called Uniterm, proposed by Mortimer Taube
Cleverdon thought it appealing and with Bob Thorne, a colleague,
did a small test
He manually indexed 200 documents using Uniterm and asked
Thorne to run some queries
This experiment put Cleverdon on a life trajectory of reliance on
experimentation for evaluating indexing systems
p. 6

Cleverdon obtained a grant from the National Science
Foundation to compare distinct indexing systems
These experiments provided interesting insights, that
culminated in the modern metrics of precision and recall
Recall ratio: the fraction of relevant documents retrieved
Precision ration: the fraction of documents retrieved that are
relevant
For instance, it became clear that, in practical
situations, the majority of searches does not require
high recall
Instead, the vast majority of the users require just a few
relevant answers
p. 7

The next step was to devise a set of experiments that
would allow evaluating each indexing system in
isolation more thoroughly
The result was a test reference collection composed
of documents, queries, and relevance judgements
It became known as the Cranfield-2 collection
The reference collection allows using the same set of
documents and queries to evaluate different ranking
systems
The uniformity of this setup allows quick evaluation of
new ranking functions
p. 8

Reference Collections
Reference collections, which are based on the
foundations established by the Cranfield experiments,
constitute the most used evaluation method in IR
A reference collection is composed of:
A set D of pre-selected documents
A set I of information need descriptions used for testing
A set of relevance judgements associated with each pair [im ,
dj ],
im ∈ I and dj ∈ D
The relevance judgement has a value of 0 if
document
dj is non-relevant to im , and 1 otherwise
These judgements are produced by human
specialists
p. 9

Precision and Recall
Consider,
I: an information request
R: the set of relevant documents for I
A: the answer set for I, generated by an IR system
R ∩ A: the intersection of the sets R and A
p. 11

The recall and precision measures are defined as
follows
Recall is the fraction of the relevant documents (the set R)
which has been retrieved i.e.,
Recall =
|R ∩ A|
|R|
Precision is the fraction of the
retrieved documents (the set
A) which is relevant i.e.,
Precision =
|R ∩ A|
|A|
p. 12

The definition of precision and recall assumes that all
docs in the set A have been examined
However, the user is not usually presented with all docs
in the answer set A at once
User sees a ranked set of documents and examines them
starting from the top
Thus, precision and recall vary as the user proceeds
with their examination of the set A
Most appropriate then is to plot a curve of precision
versus recall
p. 13

Consider a reference collection and a set of test queries
Let Rq1 be the set of relevant docs for a query q1:
Rq1 = {d3, d5, d9, d25, d39, d44, d56, d71, d89, d123}
Consider a new IR algorithm that yields the following
answer to q1 (relevant docs are marked with a bullet):
01. d123 • 06. d9 • 11. d38
02. d84 07. d511 12. d48
03. d56 • 08. d129 13. d250
04. d6 09. d187 14. d113
05. d8 10. d25 • 15. d3 •
p. 14

If we examine this ranking, we observe that
The document d123, ranked as number 1, is relevant
This document corresponds to 10% of all relevant documents
Thus, we say that we have a precision of 100% at 10% recall
The document d56, ranked as number 3, is the next relevant
At this point, two documents out of three are relevant, and two
of the ten relevant documents have been seen
Thus, we say that we have a precision of 66.6% at 20% recall
p. 15
01. d123 • 06. d9 • 11. d38
02. d84 07. d511 12. d48
03. d56 • 08. d129 13. d250
04. d6 09. d187 14. d113
05. d8 10. d25 • 15. d3 •

If we proceed with our examination of the ranking
generated, we can plot a curve of precision versus
recall as follows:
p. 16

Consider now a second query q2 whose set of relevant
answers is given by
Rq2 = {d3, d56, d129}
The previous IR algorithm processes the query q2 and
returns a ranking, as follows
01. d425 06. d615 11. d193
02. d87 07. d512 12. d715
03. d56 • 08. d129 • 13. d810
04. d32 09. d4 14. d5
05. d124 10. d130 15. d3 •
p. 17

If we examine this ranking, we observe
The first relevant document is d56
It provides a recall and precision levels equal to 33.3%
The second relevant document is d129
It provides a recall level of 66.6% (with precision equal to 25%)
The third relevant document is d3
It provides a recall level of 100% (with precision equal to 20%)
p. 18
01. d425 06. d615 11. d193
02. d87 07. d512 12. d715
03. d56 • 08. d129 • 13. d810
04. d32 09. d4 14. d5
05. d124 10. d130 15. d3 •

The precision figures at the 11 standard recall levels
are interpolated as follows
Let rj , j ∈ {0, 1, 2, . . . , 10}, be a reference to the
j-th standard recall level
Then, P (rj ) = max∀r | r j ≤r P
(r)
In our last example, this interpolation rule yields the
precision and recall figures illustrated below
p. 19

In the examples above, the precision and recall figures
have been computed for single queries
Usually, however, retrieval algorithms are evaluated by
running them for several distinct test queries
To evaluate the retrieval performance for Nq queries, we
average the precision at each recall level as follows
j
P (r ) =
Nq
Σ
i=1
i j
P (r )
Nq
where
P (rj ) is the average precision at the recall level rj
Pi (rj ) is the precision at recall level rj for the i-th
query
p. 20

To illustrate, the figure below illustrates precision-recall
figures averaged over queries q1 and q2
p. 21

Average precision-recall curves are normally used to
compare the performance of distinct IR algorithms
The figure below illustrates average precision-recall
curves for two distinct retrieval algorithms
p. 22

Precision-Recall Appropriateness
Precision and recall have been extensively used to
evaluate the retrieval performance of IR algorithms
However, a more careful reflection reveals problems
with these two measures:
First, the proper estimation of maximum recall for a query
requires detailed knowledge of all the documents in the collection
Second, in many situations the use of a single measure could be
more appropriate
Third, recall and precision measure the effectiveness over a set
of queries processed in batch mode
Fourth, for systems which require a weak ordering though, recall
and precision might be inadequate
p. 23

Single Value Summaries
Average precision-recall curves constitute standard
evaluation metrics for information retrieval systems
However, there are situations in which we would like to
evaluate retrieval performance over individual queries
The reasons are twofold:
First, averaging precision over many queries might disguise
important anomalies in the retrieval algorithms under study
Second, we might be interested in investigating whether a
algorithm outperforms the other for each query
In these situations, a single precision value can
be used
p. 24

P@5 and P@10
In the case of Web search engines, the majority of
searches does not require high recall
Higher the number of relevant documents at the top of
the ranking, more positive is the impression of the users
Precision at 5 (P@5) and at 10 (P@10) measure the
precision when 5 or 10 documents have been seen
These metrics assess whether the users are getting
relevant documents at the top of the ranking or not
p. 25

P@5 and P@10
To exemplify, consider again the ranking for the
example query q1 we have been using:
01. d123 • 06. d9 • 11. d38
02. d84 07. d511 12. d48
03. d56 • 08. d129 13. d250
04. d6 09. d187 14. d113
05. d8 10. d25 • 15. d3 •
For this query, we have P@5 = 40% and P@10 = 40%
Further, we can compute P@5 and P@10 averaged
over a sample of 100 queries, for instance
These metrics provide an early assessment of which
algorithm might be preferable in the eyes of the users
p. 26

MAP: Mean Average Precision
The idea here is to average the precision figures
obtained after each new relevant document is observed
For relevant documents not retrieved, the precision is set to 0
To illustrate, consider again the precision-recall curve
for the example query q1
The mean average precision (MAP) for q1 is given by
MAP1 =
1 + 0.66 + 0.5 + 0.4 + 0.33 + 0 + 0 + 0
+ 0 + 0 1
0
p. 27
=
0.28

R-Precision
Let R be the total number of relevant docs for a given
query
The idea here is to compute the precision at the R-th
position in the ranking
For the query q1, the R value is 10 and there are 4
relevants among the top 10 documents in the ranking
Thus, the R-Precision value for this query is 0.4
The R-precision measure is a useful for observing the
behavior of an algorithm for individual queries
Additionally, one can also compute an average
R-precision figure over a set of queries
However, using a single number to evaluate a algorithm over
several queries might be quite imprecise
p. 28

Precision Histograms
The R-precision computed for several queries can be
used to compare two algorithms as follows
Let,
RPA (i) : R-precision for algorithm A for the i-th query
RPB (i) : R-precision for algorithm B for the i-th query
Define, for instance, the difference
RPA / B (i) = RPA (i) − RPB (i)
p. 29

Precision Histograms
Figure below illustrates the RPA / B (i) values for
two retrieval algorithms over 10 example queries
The algorithm A performs better for 8 of the queries,
while the algorithm B performs better for the other 2
queries
p. 30

MRR: Mean Reciprocal Rank
MRR is a good metric for those cases in which we are
interested in the first correct answer such as
Question-Answering (QA) systems
Search engine queries that look for specific sites
URL queries
Homepage queries
p. 31

MRR: Mean Reciprocal Rank
Let,
Ri : ranking relative to a query qi
Sc o r r e c t (Ri ): position of the first correct answer in R i
Sh : threshold for ranking position
Then, the reciprocal rank RR(Ri ) for query qi is given
by
RR(Ri ) =
( 1
S correct ( R i)
0
if Sc o r re c t (Ri ) ≤ Sh
otherwise
The mean reciprocal rank (MRR) for a set Q of Nq
queries is given by
MRR(Q) =
Σ N q
i i
R R ( R
)
p. 32

The E-Measure
A measure that combines recall and precision
The idea is to allow the user to specify whether he is
more interested in recall or in precision
The E measure is defined as follows
E(j) = 1
−
1 + b2
b2
+ 1
r(j)
P (j)
where
r(j) is the recall at the j-th position in the ranking
P (j) is the precision at the j-th position in the
ranking
b ≥ 0 is a user specified parameter
E(j) is the E metric at the j-th position in the ranking
p. 33

The E-Measure
The parameter b is specified by the user and reflects
the relative importance of recall and precision
If b = 0
E(j) = 1 − P (j)
low values of b make E(j) a function of precision
If b → ∞
limb → ∞ E(j) = 1 − r(j)
high values of b make E(j) a function of recal
For b = 1, the E-measure becomes the F-measure
p. 34

F-Measure: Harmonic Mean
The F-measure is also a single measure that combines
recall and precision
F (j) =
2
1 + 1
r(j)
P (j)
where
r(j) is the recall at the j-th position in the ranking
P (j) is the precision at the j-th position in the ranking
F (j) is the harmonic mean at the j-th position in the
ranking
p. 35

F-Measure: Harmonic Mean
The function F assumes values in the interval [0, 1]
It is 0 when no relevant documents have been retrieved
and is 1 when all ranked documents are relevant
Further, the harmonic mean F assumes a high value
only when both recall and precision are high
To maximize F requires finding the best possible
compromise between recall and precision
Notice that setting b = 1 in the formula of the E-measure
yields
F (j) = 1 − E(j)
p. 36

Summary Table Statistics
Single value measures can also be stored in a table to
provide a statistical summary
For instance, these summary table statistics could
include
the number of queries used in the task
the total number of documents retrieved by all queries
the total number of relevant docs retrieved by all queries
the total number of relevant docs for all queries, as judged by the
specialists
p. 37

User-Oriented Measures
Recall and precision assume that the set of relevant
docs for a query is independent of the users
However, different users might have different relevance
interpretations
To cope with this problem, user-oriented measures
have been proposed
As before,
consider a reference collection, an information request I, and a
retrieval algorithm to be evaluated
with regard to I, let R be the set of relevant documents and A be
the set of answers retrieved
p. 38

K: set of documents known to the user
K ∩ R ∩ A: set of relevant docs that have been retrieved and
are known to the user
(R ∩ A) − K: set of relevant docs that have been retrieved but are
not known to the user
p. 39

The coverage ratio is the fraction of the documents
known and relevant that are in the answer set, that is
coverage =
|K ∩ R ∩ A|
|K ∩ R|
The novelty ratio is the fraction of the relevant docs in
the answer set that are not known to the user
novelty =
|(R ∩ A) − K|
|R ∩ A|
p. 40

A high coverage indicates that the system has found
most of the relevant docs the user expected to see
A high novelty indicates that the system is revealing
many new relevant docs which were unknown
Additionally, two other measures can be defined
relative recall: ratio between the number of relevant docs found
and the number of relevant docs the user expected to find
recall effort: ratio between the number of relevant docs the user
expected to find and the number of documents examined in an
attempt to find the expected relevant documents
p. 41

DCG — Discounted Cumulated Gain
p. 42

Discounted Cumulated Gain
Precision and recall allow only binary relevance
assessments
As a result, there is no distinction between highly
relevant docs and mildly relevant docs
These limitations can be overcome by adopting graded
relevance assessments and metrics that combine them
The discounted cumulated gain (DCG) is a metric
that combines graded relevance assessments
effectively
p. 43

When examining the results of a query, two key
observations can be made:
highly relevant documents are preferable at the top of the ranking
than mildly relevant ones
relevant documents that appear at the end of the ranking are less
valuable
p. 44

Consider that the results of the queries are graded on a
scale 0–3 (0 for non-relevant, 3 for strong relevant
docs)
For instance, for queries q1 and q2, consider that the
graded relevance scores are as follows:
Rq1 =
Rq2 =
{ [d3, 3], [d5, 3], [d9, 3], [d25, 2], [d39, 2],
[d44, 2], [d56, 1], [d71, 1], [d89, 1], [d123,
1] }
{ [d3, 3], [d56, 2], [d129, 1] }
That is, while document d3 is highly relevant to query q1,
document d56 is just mildly relevant
p. 45

Given these assessments, the results of a new ranking
algorithm can be evaluated as follows
Specialists associate a graded relevance score to the
top 10-20 results produced for a given query q
This list of relevance scores is referred to as the gain vector G
Considering the top 15 docs in the ranking produced
for queries q1 and q2, the gain vectors for these queries
are:
G1 = (1, 0, 1, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 0,
3)
G2 = (0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
3)
p. 46

By summing up the graded scores up to any point in the
ranking, we obtain the cumulated gain (CG)
For query q1, for instance, the cumulated gain at the first
position is 1, at the second position is 1+0, and so on
Thus, the cumulated gain vectors for queries q1 and q2
are given by
CG1 = (1, 1, 2, 2, 2, 5, 5, 5, 5, 7, 7, 7, 7, 7,
10)
CG2 = (0, 0, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3,
6)
For instance, the cumulated gain at position 8 of CG1 is
equal to 5
p. 47

In formal terms, we define
Given the gain vector Gj for a test query qj , the CGj
associated with it is defined as

  Gj [1] if i = 1;
CGj [i] =
  Gj [i] + CGj [i − 1] otherwise
where CGj [i] refers to the cumulated gain at the ith position
of the ranking for query qj
p. 48

We also introduce a discount factor that reduces the
impact of the gain as we move upper in the ranking
A simple discount factor is the logarithm of the ranking
position
If we consider logs in base 2, this discount factor will
be
log2 2 at position 2, log2 3 at position 3, and so on
By dividing a gain by the corresponding discount factor,
we obtain the discounted cumulated gain (DCG)
p. 49

More formally,
Given the gain vector Gj for a test query qj , the vector DCGj
associated with it is defined as

p. 50
j
DCG [i]
=


j
G [1] if i =
1;
G j [i]
log2 i + DCGj [i − 1] otherwise
where DCGj [i] refers to the discounted cumulated gain at the
ith position of the ranking for query qj

For the example queries q1 and q2, the DCG vectors are
given by
DCG1 = (1.0, 1.0, 1.6, 1.6, 1.6, 2.8, 2.8, 2.8, 2.8, 3.4, 3.4, 3.4, 3.4, 3.4,
4.2)
DCG2 = (0.0, 0.0, 1.3, 1.3, 1.3, 1.3, 1.3, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6,
2.4)
Discounted cumulated gains are much less affected by
relevant documents at the end of the ranking
By adopting logs in higher bases the discount factor can
be accentuated
p. 51

DCG Curves
To produce CG and DCG curves over a set of test
queries, we need to average them over all queries
Given a set of Nq queries, average CG[i] and
DCG[i]
over all queries are computed as follows
CG[i] =
N q
CGj
[i]
;
DCG[i] =
Σ Σ N q
j = 1 Nq j = 1
DCGj [i]
Nq
For instance, for the example queries q1 and q2, these
averages are given by
CG = (0.5, 0.5, 2.0, 2.0, 2.0, 3.5, 3.5, 4.0, 4.0, 5.0, 5.0, 5.0, 5.0, 5.0,
8.0)
DCG = (0.5, 0.5, 1.5, 1.5, 1.5, 2.1, 2.1, 2.2, 2.2, 2.5, 2.5, 2.5, 2.5, 2.5,
3.3)
p. 52

DCG Curves
Then, average curves can be drawn by varying the rank
positions from 1 to a pre-established threshold
p. 53

Ideal CG and DCG Metrics
Recall and precision figures are computed relatively to
the set of relevant documents
CG and DCG scores, as defined above, are not
computed relatively to any baseline
This implies that it might be confusing to use them
directly to compare two distinct retrieval algorithms
One solution to this problem is to define a baseline to
be used for normalization
This baseline are the ideal CG and DCG metrics, as we
now discuss
p. 54

For a given test query q, assume that the relevance
assessments made by the specialists produced:
n3 documents evaluated with a relevance score of 3
n2 documents evaluated with a relevance score of 2
n1 documents evaluated with a score of 1
n0 documents evaluated with a score of 0
The ideal gain vector IG is created by sorting all
relevance scores in decreasing order, as follows:
IG = (3, . . . , 3, 2, . . . , 2, 1, . . . , 1, 0, . . . , 0)
For instance, for the example queries q1 and q2,
we have
IG1 = (3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0,
0)
IG2 = (3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0)
p. 55

Ideal CG and ideal DCG vectors can be computed
analogously to the computations of CG and DCG
For the example queries q1 and q2, we have
ICG1 = (3, 6, 9, 11, 13, 15, 16, 17, 18, 19, 19, 19,
19, 19, 19)
ICG2
= (3, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6)
The ideal DCG vectors are given by
p. 56
IDCG1 = (3.0, 6.0, 7.9, 8.9, 9.8, 10.5, 10.9, 11.2, 11.5, 11.8, 11.8, 11.8, 11.8, 11.8,
11.8)
IDCG2 = (3.0, 5.0, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6)

Further, average ICG and average IDCG scores can
be computed as follows
ICG[i] =
N q
j=1 Nq
ICGj
[i]
;
IDCG[i] =
Σ Σ N q
j=1
IDCGj [i]
Nq
For instance, for the example queries q1 and q2, ICG
and IDCG vectors are given by
ICG = (3.0, 5.5, 7.5, 8.5, 9.5, 10.5, 11.0, 11.5, 12.0, 12.5, 12.5, 12.5, 12.5, 12.5,
12.5)
IDCG = (3.0, 5.5, 6.8, 7.3, 7.7, 8.1, 8.3, 8.4, 8.6, 8.7, 8.7, 8.7, 8.7, 8.7, 8.7)
By comparing the average CG and DCG curves for an
algorithm with the average ideal curves, we gain insight
on how much room for improvement there is
p. 57

Normalized DCG
Precision and recall figures can be directly compared to
the ideal curve of 100% precision at all recall levels
DCG figures, however, are not build relative to any ideal
curve, which makes it difficult to compare directly DCG
curves for two distinct ranking algorithms
This can be corrected by normalizing the DCG metric
Given a set of Nq test queries, normalized CG and DCG
metrics are given by
ICG[i]
NCG[i] = CG[i]
; NDCG[i] = DCG[i]
IDCG[i]
p. 58

Normalized DCG
For instance, for the example queries q1 and q2, NCG
and NDCG vectors are given by
NCG =
NDCG =
(0.17, 0.09, 0.27, 0.24, 0.21, 0.33, 0.32,
0.35, 0.33, 0.40, 0.40, 0.40, 0.40, 0.40,
0.64)
(0.17, 0.09, 0.21, 0.20, 0.19, 0.25, 0.25,
0.26, 0.26, 0.29, 0.29, 0.29, 0.29, 0.29,
0.38)
The area under the NCG and NDCG curves represent
the quality of the ranking algorithm
Higher the area, better the results are considered to
be
Thus, normalized figures can be used to compare two
distinct ranking algorithms
p. 59

Discussion on DCG Metrics
CG and DCG metrics aim at taking into account
multiple level relevance assessments
This has the advantage of distinguishing highly relevant
documents from mildly relevant ones
The inherent disadvantages are that multiple level
relevance assessments are harder and more time
consuming to generate
p. 60

Discussion on DCG Metrics
Despite these inherent difficulties, the CG and DCG
metrics present benefits:
They allow systematically combining document ranks and
relevance scores
Cumulated gain provides a single metric of retrieval performance
at any position in the ranking
It also stresses the gain produced by relevant docs up to a
position in the ranking, which makes the metrics more imune to
outliers
Further, discounted cumulated gain allows down weighting the
impact of relevant documents found late in the ranking
p. 61

BPREF — Binary Preferences
p. 62

BPREF
The Cranfield evaluation paradigm assumes that all
documents in the collection are evaluated with regard to
each query
This works well with small collections, but is not
practical with larger collections
The solution for large collections is the pooling
method
This method compiles in a pool the top results produced by
various retrieval algorithms
Then, only the documents in the pool are evaluated
The method is reliable and can be used to effectively compare the
retrieval performance of distinct systems
p. 63

BPREF
A different situation is observed, for instance, in the
Web, which is composed of billions of documents
There is no guarantee that the pooling method allows
reliably comparing distinct Web retrieval systems
The key underlying problem is that too many unseen
docs would be regarded as non-relevant
In such case, a distinct metric designed for the
evaluation of results with incomplete information is
desirable
This is the motivation for the proposal of the BPREF
metric, as we now discuss
p. 64

BPREF
Metrics such as precision-recall and P@10 consider all
documents that were not retrieved as non-relevant
For very large collections this is a problem because too
many documents are not retrieved for any single query
One approach to circumvent this problem is to use
preference relations
These are relations of preference between any two documents
retrieved, instead of using the rank positions directly
This is the basic idea used to derive the BPREF
metric
p. 65

BPREF
Bpref measures the number of retrieved docs that are
known to be non-relevant and appear before relevant
docs
The measure is called Bpref because the preference relations are
binary
The assessment is simply whether document dj is
preferable to document dk, with regard to a given
information need
To illustrate, any relevant document is preferred over
any non-relevant document for a given information need
p. 66

BPREF
J: set of all documents judged by the specialists with
regard to a given information need
R: set of docs that were found to be relevant
J − R: set of docs that were found to be non-
relevant
p. 67

BPREF
Given an information need I, let
R A : ranking computed by an IR system A relatively to I
sA , j : position of document dj in R A
[(J − R) ∧ A]|R|: set composed of the first |R|
documents in R A
that have been judged as non-relevant
p. 68

BPREF
Define
C(RA , dj ) = {dk | dk ∈ [(J − R) ∩ A]|
R|
∧ sA,k < sA,j }
as a counter of the non-relevant docs that appear
before dj in R A
Then, the BREF of ranking R A is given by
Bpref (RA ) =
1
|R|
Σ
dj ∈(R∩A) 1
−
A j
C(R ,d )
min(|R|, |(J−R)∩A|)
p. 69

BPREF
For each relevant document dj in the ranking, Bpref
accumulates a weight
This weight varies inversely with the number of judged
non-relevant docs that precede each relevant doc dj
For instance, if all |R| documents from [(J −
R) ∧ A]|R|
precede dj in the ranking, the weight
accumulated is 0
If no documents from [(J − R) ∧ A]|R| precede dj in
the ranking, the weight accumulated is 1
After all weights have been accumulated, the sum is
normalized by |R|
p. 70

BPREF
Bpref is a stable metric and can be used to compare
distinct algorithms in the context of large collections,
because
The weights associated with relevant docs are normalized
The number of judged non-relevant docs considered is equal to
the maximum number of relevant docs
p. 71

BPREF-10
Bpref is intended to be used in the presence of
incomplete information
Because that, it might just be that the number of known
relevant documents is small, even as small as 1 or 2
In this case, the metric might become unstable
Particularly if the number of preference relations available to
define N (RA , J, R, dj ) is too small
Bpref-10 is a variation of Bpref that aims at correcting
this problem
p. 72

BPREF-10
This metric ensures that a minimum of 10 preference
relations are available, as follows
Let [(J − R) ∧ A]|R|+10 be the set composed of the
first
|R| + 10 documents from (J − R) ∧ A in the ranking
Define
C1 0 (RA , dj ) = {dk | dk ∈ [(J − R) ∩ A)]|R|+10
¨
∧ s A ,k < s A , j }
¨
Then,
Bpref
10 A
(R ) = 1
|R|
Σ
d j ∈(R∩A) 1 −
C1 0 ( R A , d j )
min(|R|+10, |(J−R)∩A|)
p. 73

Rank Correlation Metrics
p. 74

Precision and recall allow comparing the relevance of
the results produced by two ranking functions
However, there are situations in which
we cannot directly measure relevance
we are more interested in determining how differently a ranking
function varies from a second one that we know well
In these cases, we are interested in comparing the
relative ordering produced by the two rankings
This can be accomplished by using statistical functions
called rank correlation metrics
p. 75

Let rankings R 1 and R2
A rank correlation metric yields a correlation coefficient
C(R1 , R2 ) with the following properties:
−1 ≤ C(R1 , R2 ) ≤ 1
if C(R1 , R2 ) = 1, the agreement between the two rankings
is perfect i.e., they are the same.
if C(R1 , R2 ) = −1, the disagreement between the two rankings
is perfect i.e., they are the reverse of each other.
if C(R1 , R2 ) = 0, the two rankings are completely independent.
increasing values of C(R1 , R2 ) imply increasing
agreement between the two rankings.
p. 76

The Spearman Coefficient
p. 77

The Spearman coefficient is likely the mostly used rank
correlation metric
It is based on the differences between the positions of a
same document in two rankings
Let
s1 , j be the position of a document dj in ranking R1 and
s2 , j be the position of dj in ranking R2
p. 78

Consider 10 example documents retrieved by two
distinct rankings R 1 and R2 . Let s1 , j and s2,j be the
document position in these two rankings, as follows:
p. 79
documents
s1,j s2,j s i,j − s2,j (s1,j − s2,j )2
d123
1 2 -1 1
d84
2 3 -1 1
d56
3 1 +2 4
d6
4 5 -1 1
d8
5 4 +1 1
d9
6 7 -1 1
d511
7 8 -1 1
d129
8 10 -2 4
d187
9 6 +3 9
d25 10 9 +1 1
Sum of Square Distances 24

By plotting the rank positions for R 1 and R2 in a
2-dimensional coordinate system, we observe that
there is a strong correlation between the two rankings
p. 80

To produce a quantitative assessment of this
correlation, we sum the squares of the differences for
each pair of rankings
If there are K documents ranked, the maximum value
for the sum of squares of ranking differences is given by
K × (K2 − 1)
3
Let K = 10
If the two rankings were in perfect disagreement, then this value
is (10 × (102 − 1))/3, or 330
On the other hand, if we have a complete agreement the sum is
0
p. 81

Let us consider the fraction
Σ K
j=1 (s1,j − s2,j )2
K×(K2 −1)
3
Its value is
0 when the two rankings are in perfect agreement
+1 when they are in perfect disagreement
If we multiply the fraction by 2, its value shifts to the
range [0, +2]
If we now subtract the result from 1, the resultant value
shifts to the range [−1, +1]
p. 82

This reasoning suggests defining the correlation
between the two rankings as follows
Let s1 , j and s2,j be the positions of a document dj in two
rankings R 1 and R2 , respectively
Define
S(R1 , R2 ) = 1
−
6
×
Σ K
j=1 (s1,j −s2,j )2
K×(K2 −1)
where
S(R1 , R2 ) is the Spearman rank correlation
coefficient
K indicates the size of the ranked sets
p. 83

For the rankings in Figure below, we have
S(R1 , R2 ) = 1
−
6 ×
24
10 × (102 −
1)
990
p. 84
144
= 1 − =
0.854
documents
s1,j s2,j s i,j − s2,j (s1,j − s2,j )2
d123
1 2 -1 1
d84
2 3 -1 1
d56
3 1 +2 4
d6
4 5 -1 1
d8
5 4 +1 1
d9
6 7 -1 1
d511
7 8 -1 1
d129
8 10 -2 4
d187
9 6 +3 9
d25 10 9 +1 1
Sum of Square Distances 24

The Kendall Tau Coefficient
p. 85

It is difficult to assign an operational interpretation to
Spearman coefficient
One alternative is to use a coefficient that has a natural
and intuitive interpretation, as the Kendall Tau
coefficient
p. 86

When we think of rank correlations, we think of how two
rankings tend to vary in similar ways
To illustrate, consider two documents dj and dk and
their positions in the rankings R 1 and R2
Further, consider the differences in rank positions for
these two documents in each ranking, i.e.,
s1,k
s2,k
—
—
s1,j
s2,j
If these differences have the same sign, we say that the
document pair [dk, dj ] is concordant in both rankings
If they have different signs, we say that the document
pair is discordant in the two rankings
p. 87

Consider the top 5 documents in rankings R 1 and R2
documents
s1,j s2,j s i,j − s2,j
d123
1 2 -1
d84
2 3 -1
d56
3 1 +2
d6
4 5 -1
d8
5 4 +1
The ordered document pairs in ranking R 1 are
[d123, d84], [d123, d56],
[d123, d6], [d123, d8],
[d84, d56], [d84, d6], [d84,
d8],
[d56, d6], [d56, d8],
[d6, d8]
p. 88
2
for a total of 1 × 5 × 4, or 10 ordered pairs

Repeating the same exercise for the top 5 documents in
ranking R2 , we obtain
[d56, d123], [d56, d84], [d56, d8], [d56,
d6],
[d123, d84], [d123, d8],
[d84, d8], [d84, d6],
[d123, d6],
[d8, d6]
We compare these two sets of ordered pairs looking for
concordant and discordant pairs
p. 89

Let us mark with a C the concordant pairs and with a D
the discordant pairs
For ranking R1 , we have
C, D, C, C,
D, C,
C, C, C,
D
For ranking R2 , we have
D, D,
C, C,
C, C,
C, C,
C,
D
p. 90

That is, a total of 20, i.e., K ( K — 1), ordered pairs
are produced jointly by the two rankings
Among these, 14 pairs are concordant and 6 pairs are
discordant
The Kendall Tau coefficient is defined as
τ (Y1 , Y2 ) = P (Y1 = Y2 ) — P (Y1 /= Y2 )
In our example
14
6
τ (Y1 , Y2 ) =
20
—
20
=
p. 91

Let,
∆(Y1, Y2 ): number of discordant document pairs in Y1 and Y2
K( K — 1) — ∆(Y1, Y2 ): number of concordant document pairs
in
Y1 and Y2
Then,
P (Y1 = Y2 ) =
P (Y1 /= Y2 ) =
K ( K — 1) — ∆(Y1 ,
Y2 ) K ( K —
1)
∆(Y1 , Y2 )
K ( K —
1)
which yields τ (Y1 , Y2 ) = 1
—
×
2 ∆(R ,R )
1
2
K(K
−1)
p. 92

2 ×
6
For the case of our previous example, we have
∆(Y1, Y2 ) = 6
K = 5
Thus,
τ (Y1 , Y2 ) = 1 —
5(5 — 1)
= 0.4
as before
The Kendall Tau coefficient is defined only for rankings
over a same set of elements
Most important, it has a simpler algebraic structure than
the Spearman coefficient
p. 93

Reference Collections
With small collections one can apply the Cranfield
evaluation paradigm to provide relevance assessments
With large collections, however, not all documents can
be evaluated relatively to a given information need
The alternative is consider only the top k documents
produced by various ranking algorithms for a given
information need
This is called the pooling method
The method works for reference collections of a few
million documents, such as the TREC collections
p. 95

The TREC Conferences
TREC is an yearly promoted conference dedicated to
experimentation with large test collections
For each TREC conference, a set of experiments is
designed
The research groups that participate in the conference
use these experiments to compare their retrieval
systems
As with most test collections, a TREC collection is
composed of three parts:
the documents
the example information requests (called topics)
a set of relevant documents for each example information
request
p. 97

The Document Collections
The main TREC collection has been growing steadily
over the years
The TREC-3 collection has roughly 2 gigabytes
The TREC-6 collection has roughly 5.8 gigabytes
It is distributed in 5 CD-ROM disks of roughly 1 gigabyte of
compressed text each
Its 5 disks were also used at the TREC-7 and TREC-8
conferences
The Terabyte test collection introduced at TREC-15,
also referred to as GOV2, includes 25 million Web
documents crawled from sites in the “.gov” domain
p. 98

TREC documents come from the following sources:
WSJ → Wall Street Journal
AP → Associated Press (news wire)
ZIFF → Computer Selects (articles), Ziff-
Davis FR → Federal Register
DOE → US DOE Publications (abstracts)
SJMN → San Jose Mercury News
PAT → US Patents
FT → Financial Times
CR → Congressional Record
FBIS → Foreign Broadcast Information
Service LAT → LA Times
p. 99

Contents of TREC-6 disks 1 and 2
p. 100
Disk Contents Size
Mb
Number
Docs
Words/Doc.
(median)
Words/Doc.
(mean)
1 WSJ, 1987-1989 267 98,732 245 434.0
AP, 1989 254 84,678 446 473.9
ZIFF 242 75,180 200 473.0
FR, 1989 260 25,960 391 1315.9
DOE 184 226,087 111 120.4
2 WSJ, 1990-1992 242 74,520 301 508.4
AP, 1988 237 79,919 438 468.7
ZIFF 175 56,920 182 451.9
FR, 1988 209 19,860 396 1378.1

Contents of TREC-6 disks 3-6
p. 101
Disk Contents Size
Mb
Number
Docs
Words/Doc.
(median)
Words/Doc.
(mean)
3 SJMN, 1991 287 90,257 379 453.0
AP, 1990 237 78,321 451 478.4
ZIFF 345 161,021 122 295.4
PAT
, 1993 243 6,711 4,445 5391.0
4 FT, 1991-1994 564 210,158 316 412.7
FR, 1994 395 55,630 588 644.7
CR, 1993 235 27,922 288 1373.5
5 FBIS 470 130,471 322 543.6
LAT 475 131,896 351 526.5
6 FBIS 490 120,653 348 581.3

Documents from all subcollections are tagged with
SGML to allow easy parsing
Some structures are common to all documents:
The document number, identified by <DOCNO>
The field for the document text, identified by <TEXT>
Minor structures might be different across
subcollections
p. 102

An example of a TREC document in the Wall Street
Journal subcollection
<doc>
<docno> WSJ880406-0090 </docno>
<hl> AT&T Unveils Services to Upgrade Phone Networks
Under Global Plan </hl>
<author> Janet Guyon (WSJ Staff) </author>
<dateline> New York </dateline>
<text>
American Telephone & Telegraph Co introduced the first
of a new generation of phone services with broad . . .
</text>
</doc>
p. 103

The TREC Web Collections
A Web Retrieval track was introduced at TREC-9
The VLC2 collection is from an Internet Archive crawl of 1997
WT2g and WT10g are subsets of the VLC2 collection
.GOV is from a crawl of the .gov Internet done in 2002
.GOV2 is the result of a joint NIST/UWaterloo effort in 2004
p. 104
Collection # Docs Avg Doc Size Collection Size
VLC2 (WT100g) 18,571,671 5.7 KBytes 100 GBytes
WT2g 247,491 8.9 KBytes 2.1 GBytes
WT10g 1,692,096 6.2 KBytes 10 GBytes
.GOV 1,247,753 15.2 KBytes 18 GBytes
.GOV2 27 million 15 KBytes 400 GBytes

Information Requests Topics
Each TREC collection includes a set of example
information requests
Each request is a description of an information need in
natural language
In the TREC nomenclature, each test information
request is referred to as a topic
p. 105

An example of an information request is the topic
numbered 168 used in TREC-3:
<top>
<num> Number: 168
<title> Topic: Financing AMTRAK
<desc> Description:
A document will address the role of the Federal Government in
financing the operation of the National Railroad Transportation
Corporation (AMTRAK)
<narr> Narrative: A relevant document must provide
information on
the government’s responsibility to make AMTRAK an economically viable
entity. It could also discuss the privatization of AMTRAK as an
alternative to continuing government subsidies. Documents comparing
government subsidies given to air and bus transportation with those
provided to AMTRAK would also be relevant
</top>
p. 106

The task of converting a topic into a system query is
considered to be a part of the evaluation procedure
The number of topics prepared for the first eight TREC
conferences is 450
p. 107

The Relevant Documents
The set of relevant documents for each topic is obtained
from a pool of possible relevant documents
This pool is created by taking the top K documents (usually,
K = 100) in the rankings generated by various retrieval systems
The documents in the pool are then shown to human assessors
who ultimately decide on the relevance of each document
This technique of assessing relevance is called the
pooling method and is based on two assumptions:
First, that the vast majority of the relevant documents is collected
in the assembled pool
Second, that the documents which are not in the pool can be
considered to be not relevant
p. 108

The Benchmark Tasks
The TREC conferences include two main information
retrieval tasks
Ad hoc task: a set of new requests are run against a fixed
document database
routing task: a set of fixed requests are run against a database
whose documents are continually changing
For the ad hoc task, the participant systems execute the
topics on a pre-specified document collection
For the routing task, they receive the test information
requests and two distinct document collections
The first collection is used for training and allows the tuning of the
retrieval algorithm
The second is used for testing the tuned retrieval algorithm
p. 109

The Benchmark Tasks
Starting at the TREC-4 conference, new secondary
tasks were introduced
At TREC-6, secondary tasks were added in as
follows:
Chinese — ad hoc task in which both the documents and the
topics are in Chinese
Filtering — routing task in which the retrieval algorithms has only to
decide whether a document is relevant or not
Interactive — task in which a human searcher interacts with the
retrieval system to determine the relevant documents
NLP — task aimed at verifying whether retrieval algorithms based on
natural language processing offer advantages when compared to
the more traditional retrieval algorithms based on index terms
p. 110

The Benchmark Tasks
Other tasks added in TREC-6:
Cross languages — ad hoc task in which the documents are in
one language but the topics are in a different language
High precision — task in which the user of a retrieval system is
asked to retrieve ten documents that answer a given information
request within five minutes
Spoken document retrieval — intended to stimulate research
on retrieval techniques for spoken documents
Very large corpus — ad hoc task in which the retrieval systems
have to deal with collections of size 20 gigabytes
p. 111

The Benchmark Tasks
The more recent TREC conferences have focused on
new tracks that are not well established yet
The motivation is to use the experience at these tracks to develop
new reference collections that can be used for further research
At TREC-15, the main tracks were question answering,
genomics, terabyte, enterprise, spam, legal, and blog
p. 112

Evaluation Measures at TREC
At the TREC conferences, four basic types of evaluation
measures are used:
Summary table statistics — this is a table that summarizes
statistics relative to a given task
Recall-precision averages — these are a table or graph with
average precision (over all topics) at 11 standard recall levels
Document level averages — these are average precision
figures computed at specified document cutoff values
Average precision histogram — this is a graph that includes a
single measure for each separate topic
p. 113

Other Reference Collections
Inex
Reuters
OHSUMED
NewsGrou
ps
NTCIR
CLEF
Small
collecti
ons
ADI,
CAC
M,
ISI,
CRA p. 114

INEX Collection
INitiative for the Evaluation of XML Retrieval
It is a test collection designed specifically for evaluating
XML retrieval effectiveness
It is of central importance for the XML community
p. 115

Reuters, OHSUMED, NewsGroups
Reuters
A reference collection composed of news articles published by
Reuters
It contains more than 800 thousand documents organized in 103
topical categories.
OHSUMED
A reference collection composed of medical references from the
Medline database
It is composed of roughly 348 thousand medical references,
selected from 270 journals published in the years 1987-1991
p. 116

Reuters, OHSUMED, NewsGroups
NewsGroups
Composed of thousands of newsgroup messages organized
according to 20 groups
These three collections contain information on
categories (classes) associated with each document
Thus, they are particularly suitable for the evaluation of
text classification algorithms
p. 117

NTCIR Collections
NII Test Collection for IR Systems
It promotes yearly workshops code-named NTCIR
Workshops
For these workshops, various reference collections composed of
patents in Japanese and English have been assembled
To illustrate, the NTCIR-7 PATMT (Patent Translation
Test) collection includes:
1.8 million translated sentence pairs (Japanese-English)
5,200 test sentence pairs
124 queries
human judgements for the translation results
p. 118

CLEF Collections
CLEF is an annual conference focused on
Cross-Language IR (CLIR) research and related issues
For supporting experimentation, distinct CLEF
reference collections have been assembled over the
years
p. 119

Other Small Test Collections
Many small test collections have been used by the IR
community over the years
They are no longer considered as state of the art test
collections, due to their small sizes
Collection Subject Num Docs Num Queries
ADI Information Science 82 35
CACM Computer Science 3200 64
ISI Library Science 1460 76
CRAN Aeronautics 1400 225
LISA Library Science 6004 35
MED Medicine 1033 30
NLM Medicine 3078 155
NPL Elec Engineering 11,429 100
TIME General Articles 423 83
p. 120

Other Small Test Collections
Another small test collection of interest is the Cystic
Fibrosis (CF) collection
It is composed of:
1,239 documents indexed with the term ‘cystic fibrosis’ in the
MEDLINE database
100 information requests, which have been generated by an
expert with research experience with cystic fibrosis
Distinctively, the collection includes 4 separate
relevance scores for each relevant document
p. 121

User Based Evaluation
User preferences are affected by the characteristics of
the user interface (UI)
For instance, the users of search engines look first at
the upper left corner of the results page
Thus, changing the layout is likely to affect the
assessment made by the users and their behavior
Proper evaluation of the user interface requires going
beyond the framework of the Cranfield experiments
p. 123

Human Experimentation in the Lab
Evaluating the impact of UIs is better accomplished in
laboratories, with human subjects carefully selected
The downside is that the experiments are costly to
setup and costly to be repeated
Further, they are limited to a small set of information
needs executed by a small number of human subjects
However, human experimentation is of value because it
complements the information produced by evaluation
based on reference collections
p. 124

Side-by-Side Panels
A form of evaluating two different systems is to evaluate
their results side by side
Typically, the top 10 results produced by the systems for
a given query are displayed in side-by-side panels
Presenting the results side by side allows controlling:
differences of opinion among subjects
influences on the user opinion produced by the ordering of the
top results
p. 126

Side-by-Side Panels
Side by side panels for Yahoo! and Google
Top 5 answers produced by each search engine, with regard to
the query “information retrieval evaluation”
p. 127

Side-by-Side Panels
The side-by-side experiment is simply a judgement on
which side provides better results for a given query
By recording the interactions of the users, we can infer which of
the answer sets are preferred to the query
Side by side panels can be used for quick comparison
of distinct search engines
p. 128

Side-by-Side Panels
In a side-by-side experiment, the users are aware that
they are participating in an experiment
Further, a side-by-side experiment cannot be repeated
in the same conditions of a previous execution
Finally, side-by-side panels do not allow measuring how
much better is system A when compared to system B
Despite these disadvantages, side-by-side panels
constitute a dynamic evaluation method that provides
insights that complement other evaluation methods
p. 129

A/B Testing & Crowdsourcing
p. 130

A/B Testing
A/B testing consists of displaying to selected users a
modification in the layout of a page
The group of selected users constitute a fraction of all users such
as, for instance, 1%
The method works well for sites with large audiences
By analysing how the users react to the change, it is
possible to analyse if the modification proposed is
positive or not
A/B testing provides a form of human experimentation,
even if the setting is not that of a lab
p. 131

Crowdsourcing
There are a number of limitations with current
approaches for relevance evaluation
For instance, the Cranfield paradigm is expensive and
has obvious scalability issues
Recently, crowdsourcing has emerged as a feasible
alternative for relevance evaluation
Crowdsourcing is a term used to describe tasks that are
outsourced to a large group of people, called “workers”
It is an open call to solve a problem or carry out a task,
one which usually involves a monetary value in
exchange for such service
p. 132

Crowdsourcing
To illustrate, crowdsourcing has been used to validate
research on the quality of search snippets
One of the most important aspects of crowdsourcing is
to design the experiment carefully
It is important to ask the right questions and to use
well-known usability techniques
Workers are not information retrieval experts, so the
task designer should provide clear instructions
p. 133

Amazon Mechanical Turk
Amazon Mechanical Turk (AMT) is an example of a
crowdsourcing platform
The participants execute human intelligence tasks,
called HITs, in exchange for small sums of money
The tasks are filed by requesters who have an
evaluation need
While the identity of participants is not known to
requesters, the service produces evaluation results of
high quality
p. 134

Evaluation using Clickthrough Data
p. 135

Evaluation w/ Clickthrough Data
Reference collections provide an effective means of
evaluating the relevance of the results set
However, they can only be applied to a relatively small
number of queries
On the other side, the query log of a Web search
engine is typically composed of billions of queries
Thus, evaluation of a Web search engine using reference
collections has its limitations
p. 136

Evaluation w/ Clickthrough Data
One very promising alternative is evaluation based on
the analysis of clickthrough data
It can be obtained by observing how frequently the
users click on a given document, when it is shown in
the answer set for a given query
This is particularly attractive because the data can be
collected at a low cost without overhead for the user
p. 137

Biased Clickthrough Data
To compare two search engines A and B , we can
measure the clickthrough rates in rankings Y A and Y B
To illustrate, consider that a same query is specified by
various users in distinct moments in time
We select one of the two search engines randomly and
show the results for this query to the user
By comparing clickthrough data over millions of queries,
we can infer which search engine is preferable
p. 138

However, clickthrough data is difficult to interpret
To illustrate, consider a query q and assume that the
users have clicked
on the answers 2, 3, and 4 in the ranking Y A , and
on the answers 1 and 5 in the ranking Y B
In the first case, the average clickthrough rank position
is (2+3+4)/3, which is equal to 3
In the second case, it is (1+5)/2, which is also equal to
3
The example shows that clickthrough data is difficult to
analyze
p. 139

Further, clickthrough data is not an absolute indicator of
relevance
That is, a document that is highly clicked is not
necessarily relevant
Instead, it is preferable with regard to the other
documents in the answer
Further, since the results produced by one search
engine are not relative to the other, it is difficult to use
them to compare two distinct ranking algorithms directly
The alternative is to mix the two rankings to collect
unbiased clickthrough data, as follows
p. 140

Unbiased Clickthrough Data
To collect unbiased clickthrough data from the users,
we mix the result sets of the two ranking algorithms
This way we can compare clickthrough data for the two
rankings
To mix the results of the two rankings, we look at the top
results from each ranking and mix them
p. 141

The algorithm below achieves the effect of mixing
rankings Y A and Y B
Input: Y A = (a1, a2, . . .), Y B = (b1, b2, . . .).
Output: a combined ranking Y.
combine_ranking(YA , Y B , ka , kb, Y)
{ if (ka = kb) {
if (YA [ka + 1] /
∈ Y)
{ Y := Y + YA [ka + 1]
}
combine_ranking(YA , Y B , ka + 1,
kb, Y)
} else {
if (YB [kb + 1] /
∈ Y)
{ Y := Y + Y B [kb + 1]
p. 142

Notice that, among any set of top r ranked answers, the
number of answers originary from each ranking differs
by no more than 1
By collecting clickthrough data for the combined
ranking, we further ensure that the data is unbiased and
reflects the user preferences
p. 143

Under mild conditions, it can be shown that
Ranking Y A contains more relevant documents
than ranking Y B only if the clickthrough rate for
Y A is higher than the clickthrough rate for YB .
Most important, under mild assumptions, the
comparison of two ranking algorithms with basis
on the combined ranking clickthrough data is
consistent with a comparison of them based on
relevance judgements collected from human
assessors.
This is a striking result that shows the correlation
between clicks and the relevance of results
p. 144

p. 1
Chapter 5
Relevance Feedback and
Query Expansion
Introduction
A Framework for Feedback Methods
Explicit Relevance Feedback
Explicit Feedback Through Clicks
Implicit Feedback Through Local Analysis
Implicit Feedback Through Global Analysis
Trends and Research Issues

Introduction
Most users find it difficult to formulate queries that are
well designed for retrieval purposes
Yet, most users often need to reformulate their queries
to obtain the results of their interest
Thus, the first query formulation should be treated as an initial
attempt to retrieve relevant information
Documents initially retrieved could be analyzed for relevance and
used to improve initial query
p. 2

Introduction
The process of query modification is commonly referred
as
relevance feedback, when the user provides information on
relevant documents to a query, or
query expansion, when information related to the query is used
to expand it
We refer to both of them as feedback methods
Two basic approaches of feedback methods:
explicit feedback, in which the information for query
reformulation is provided directly by the users, and
implicit feedback, in which the information for query
reformulation is implicitly derived by the system
p. 3

A Framework for Feedback
Methods
p. 4

A Framework
Consider a set of documents Dr that are known to be
relevant to the current query q
In relevance feedback, the documents in Dr are used to
transform q into a modified query qm
However, obtaining information on documents relevant
to a query requires the direct interference of the user
Most users are unwilling to provide this information, particularly in
the Web
p. 5

A Framework
Because of this high cost, the idea of relevance
feedback has been relaxed over the years
Instead of asking the users for the relevant documents,
we could:
Look at documents they have clicked on; or
Look at terms belonging to the top documents in the result set
In both cases, it is expect that the feedback cycle will
produce results of higher quality
p. 6

A Framework
A feedback cycle is composed of two basic steps:
Determine feedback information that is either related or expected
to be related to the original query q and
Determine how to transform query q to take this information
effectively into account
The first step can be accomplished in two distinct
ways:
Obtain the feedback information explicitly from the users
Obtain the feedback information implicitly from the query results
or from external sources such as a thesaurus
p. 7

A Framework
In an explicit relevance feedback cycle, the feedback
information is provided directly by the users
However, collecting feedback information is expensive
and time consuming
In the Web, user clicks on search results constitute a
new source of feedback information
A click indicate a document that is of interest to the user
in the context of the current query
Notice that a click does not necessarily indicate a document that
is relevant to the query
p. 8

Explicit Feedback Information
p. 9

A Framework
In an implicit relevance feedback cycle, the feedback
information is derived implicitly by the system
There are two basic approaches for compiling implicit
feedback information:
local analysis, which derives the feedback information from the
top ranked documents in the result set
global analysis, which derives the feedback information from
external sources such as a thesaurus
p. 10

Implicit Feedback Information
p. 11

p. 12

In a classic relevance feedback cycle, the user
is presented with a list of the retrieved
documents
Then, the user examines them and marks those that
are relevant
In practice, only the top 10 (or 20) ranked documents
need to be examined
The main idea consists of
selecting important terms from the documents that have been
identified as relevant, and
enhancing the importance of these terms in a new query
formulation
p. 13

Expected effect: the new query will be moved towards
the relevant docs and away from the non-relevant ones
Early experiments have shown good improvements in
precision for small test collections
Relevance feedback presents the following
characteristics:
it shields the user from the details of the query reformulation
process (all the user has to provide is a relevance judgement)
it breaks down the whole searching task into a sequence of small
steps which are easier to grasp
p. 14

The Rocchio Method
Documents identified as relevant (to a given query)
have similarities among themselves
Further, non-relevant docs have term-weight vectors
which are dissimilar from the relevant documents
The basic idea of the Rocchio Method is to reformulate
the query such that it gets:
closer to the neighborhood of the relevant documents in the
vector space, and
away from the neighborhood of the non-relevant documents
p. 16

The Rocchio Method
Let us define terminology regarding the processing of a
given query q, as follows:
Dr : set of relevant documents among the documents retrieved
Nr : number of documents in set Dr
Dn : set of non-relevant docs among the documents retrieved
Nn : number of documents in set Dn
Cr : set of relevant docs among all documents in the collection
N : number of documents in the collection
α, β, γ: tuning constants
p. 17

The Rocchio Method
Consider that the set Cr is known in advance
Then, the best query vector for distinguishing the
relevant from the non-relevant docs is given by
1
→qopt = r
|C
|
→
6d ∈C
1
d→j −
r
N − |C
|
Σ Σ
→
6d
/∈C
j r j r
d
→
j
where
|Cr | refers to the cardinality of the set Cr
d→j is a weighted term vector associated with document dj ,
and
→qopt is the optimal weighted term vector for query q
p. 18

The Rocchio Method
However, the set Cr is not known a priori
To solve this problem, we can formulate an initial query
and to incrementally change the initial query vector
p. 19

The Rocchio Method
There are three classic and similar ways to calculate
the modified query →qm as follows,
p. 20
m
Standard_Rocchio : →q = α →q
+
β
Nr
j
∀d→
∈D
r
d
→
j —
γ
Σ Σ
Nn
j
∀d→
∈D
n
d
→
j
Ide_Regular : →qm = α →q
+ β
Σ
∀d→j
∈Dr
d
→
j
— γ
Σ
∀d→j
∈Dn
d
→
j
Ide_Dec_Hi : →qm = α →q
+ β
Σ
∀d→j
∈Dr
d
→
j
— γ max_rank(Dn )
where max_rank(Dn) is the highest ranked
non-relevant doc

The Rocchio Method
Three different setups of the parameters in the Rocchio
formula are as follows:
α = 1, proposed by Rocchio
α = β = γ = 1, proposed by Ide
γ = 0, which yields a positive feedback strategy
The current understanding is that the three techniques yield
similar results
The main advantages of the above relevance feedback
techniques are simplicity and good results
Simplicity: modified term weights are computed directly from the
set of retrieved documents
Good results: the modified query vector does reflect a portion of
the intended query semantics (observed experimentally)
p. 21

Relevance Feedback for the Probabilistic
Model
p. 22

A Probabilistic Method
The probabilistic model ranks documents for a query q
according to the probabilistic ranking principle
The similarity of a document dj to a query q in the
probabilistic model can be expressed as
Σ
sim(dj , q) α
log ki∈q∧ki∈dj
P (ki|
R)
1 − P (ki|
R)
P (ki|
R)
1 − P (ki|R)
+ log
where
P (ki |R) stands for the probability of observing the term ki in
the set R of relevant documents
P (ki |R) stands for the probability of observing the term ki in
the set R of non-relevant docs
p. 23

Initially, the equation above cannot be used because
P (ki|R) and P (ki|R) are unknown
Different methods for estimating these probabilities
automatically were discussed in Chapter 3
With user feedback information, these probabilities are
estimated in a slightly different way
For the initial search (when there are no retrieved
documents yet), assumptions often made include:
P (ki |R) is constant for all terms ki (typically 0.5)
the term probability distribution P (ki |R) can be approximated
by the distribution in the whole collection
p. 24

These two assumptions yield:
i
P (ki|R) = 0.5 P (k |R)
=
ni
N
where ni stands for the number of documents in the
collection that contain the term ki
Substituting into similarity equation, we obtain
initial
sim (dj, q)
=
Σ
ki∈q∧ki∈dj
N − ni
log
ni
For the feedback searches, the accumulated statistics
on relevance are used to evaluate P (ki|R) and P (ki|
R)
p. 25

Let nr,i be the number of documents in set Dr that
contain the term ki
Then, the probabilities P (ki|R) and P (ki|R) can
be approximated by
P (ki|R)
=
nr,i
Nr
i
P (k |R)
=
ni − nr,i
N − Nr
Using these approximations, the similarity equation can
rewritten as
j
sim(d , q)
=
Σ
k i ∈q∧ki∈dj
lo
g
nr,i
N r − nr,i n i − nr,i
p. 26
N − Nr − (ni − nr, i )
+ log

Notice that here, contrary to the Rocchio Method, no
query expansion occurs
The same query terms are reweighted using feedback
information provided by the user
The formula above poses problems for certain small
values of Nr and nr,i
For this reason, a 0.5 adjustment factor is often added
to the estimation of P (ki|R) and P (ki|R):
i
P (k
|
R)
=
r,i
n +
0.5
Nr +
1
i
P (k |R)
=
ni − nr,i +
0.5
N − Nr + 1
p. 27

The main advantage of this feedback method is the
derivation of new weights for the query terms
The disadvantages include:
document term weights are not taken into account during the
feedback loop;
weights of terms in the previous query formulations are
disregarded; and
no query expansion is used (the same set of index terms in the
original query is reweighted over and over again)
Thus, this method does not in general operate as
effectively as the vector modification methods
p. 28

Evaluation of Relevance Feedback
p. 29

Evaluation of Relevance Feedback
Consider the modified query vector →qm produced by
expanding →q with relevant documents, according to
the Rocchio formula
Evaluation of →qm:
Compare the documents retrieved by →qm with the set of
relevant documents for →q
In general, the results show spectacular improvements
However, a part of this improvement results from the higher ranks
assigned to the relevant docs used to expand →q into q→m
Since the user has seen these docs already, such evaluation is
unrealistic
p. 30

The Residual Collection
A more realistic approach is to evaluate →qm
considering only the residual collection
We call residual collection the set of all docs minus the set of
feedback docs provided by the user
Then, the recall-precision figures for →qm tend to be
lower than the figures for the original query vector →q
This is not a limitation because the main purpose of the
process is to compare distinct relevance feedback
strategies
p. 31

p. 32

Web search engine users not only inspect the answers
to their queries, they also click on them
The clicks reflect preferences for particular answers in
the context of a given query
They can be collected in large numbers without
interfering with the user actions
The immediate question is whether they also reflect
relevance judgements on the answers
Under certain restrictions, the answer is affirmative as
we now discuss
p. 33

Eye Tracking
Clickthrough data provides limited information on the
user behavior
One approach to complement information on user
behavior is to use eye tracking devices
Such commercially available devices can be used to
determine the area of the screen the user is focussed in
The approach allows correctly detecting the area of the
screen of interest to the user in 60-90% of the cases
Further, the cases for which the method does not work
can be determined
p. 34

Eye Tracking
Eye movements can be classified in four types:
fixations, saccades, pupil dilation, and scan paths
Fixations are a gaze at a particular area of the screen
lasting for 200-300 milliseconds
This time interval is large enough to allow effective brain
capture and interpretation of the image displayed
Fixations are the ocular activity normally associated
with visual information acquisition and processing
That is, fixations are key to interpreting user
behavior
p. 35

Relevance Judgements
To evaluate the quality of the results, eye tracking is
not appropriate
This evaluation requires selecting a set of test queries
and determining relevance judgements for them
This is also the case if we intend to evaluate the quality
of the signal produced by clicks
p. 36

User Behavior
Eye tracking experiments have shown that users scan
the query results from top to bottom
The users inspect the first and second results right
away, within the second or third fixation
Further, they tend to scan the top 5 or top 6 answers
thoroughly, before scrolling down to see other answers
p. 37

User Behavior
Percentage of times each one of the top results was
viewed and clicked on by a user, for 10 test tasks and
29 subjects (Thorsten Joachims et al)
p. 38

User Behavior
We notice that the users inspect the top 2 answers
almost equally, but they click three times more in the
first
This might be indicative of a user bias towards the
search engine
That is, that the users tend to trust the search engine in
recommending a top result that is relevant
p. 39

User Behavior
This can be better understood by presenting test
subjects with two distinct result sets:
the normal ranking returned by the search engine and
a modified ranking in which the top 2 results have their positions
swapped
Analysis suggest that the user displays a trust bias in
the search engine that favors the top result
That is, the position of the result has great influence on
the user’s decision to click on it
p. 40

Clicks as a Metric of Preferences
Thus, it is clear that interpreting clicks as a direct
indicative of relevance is not the best approach
More promising is to interpret clicks as a metric of user
preferences
For instance, a user can look at a result and decide to
skip it to click on a result that appears lower
In this case, we say that the user prefers the result
clicked on to the result shown upper in the ranking
This type of preference relation takes into account:
the results clicked on by the user
the results that were inspected and not clicked on
p. 41

Clicks within a Same Query
To interpret clicks as user preferences, we adopt the
following definitions
Given a ranking function R(qi, dj ), let rk be the kth ranked
result
That is, r1, r2, r3 stand for the first, the second, and the third top
results, respectively
Further, let
√
rk indicate that the user has clicked on the kt h
result
Define a preference function rk > rk − n , 0 < k − n < k, that
states that, according to the click actions of the user, the kth top
result is preferrable to the (k − n)th result
p. 42

To illustrate, consider the following example regarding
the click behavior of a user:
√
r3
√
r5
r1 r2 r4 r6 r7 r8 r9 √
r10
This behavior does not allow us to make definitive
statements about the relevance of results r3, r5, and r10
However, it does allow us to make statements on the
relative preferences of this user
Two distinct strategies to capture the preference
relations in this case are as follows.
Skip-Above: if
√
rk then rk > rk − n , for all rk − n that was
not clicked
Skip-Previous: if
√
rk and rk−1 has not been clicked then rk
p. 43
> rk−1

To illustrate, consider again the following example
regarding the click behavior of a user:
r1 r2
√
r3 r4
√
r5 r6 r7 r8
r9
√
r10
According to the Skip-Above strategy, we have:
r3 > r2; r3 > r1
And, according to the Skip-Previous strategy, we have:
r3 > r2
We notice that the Skip-Above strategy produces more
preference relations than the Skip-Previous strategy
p. 44

Empirical results indicate that user clicks are in
agreement with judgements on the relevance of results
in roughly 80% of the cases
Both the Skip-Above and the Skip-Previous strategies produce
preference relations
If we swap the first and second results, the clicks still reflect
preference relations, for both strategies
If we reverse the order of the top 10 results, the clicks still reflect
preference relations, for both strategies
Thus, the clicks of the users can be used as a strong
indicative of personal preferences
Further, they also can be used as a strong indicative of
the relative relevance of the results for a given query
p. 45

Clicks within a Query Chain
The discussion above was restricted to the context of a
single query
However, in practice, users issue more than one query
in their search for answers to a same task
The set of queries associated with a same task can be
identified in live query streams
This set constitute what is referred to as a query chain
The purpose of analysing query chains is to produce
new preference relations
p. 46

To illustrate, consider that two result sets in a same
query chain led to the following click actions:
√
s2 s3 s4 s5
5 6 r7 r8 r9 r10
s6 s7
s8 s9
r1 r2 r3 r4 r
r
s1
√
where
s10
rj refers to an answer in the first result set
sj refers to an answer in the second result set
In this case, the user only clicked on the second and
fifth answers of the second result set
p. 47

Two distinct strategies to capture the preference relations
in this case, are as follows
Top-One-No-Click-Earlier: if ∃ sk |
√
sk then sj > r1, for j ≤ 10.
Top-Two-No-Click-Earlier: if ∃ sk |
√
sk then sj > r1 and sj > r2,
for
j ≤ 10
According the first strategy, the following preferences are
produced by the click of the user on result s2:
s1 > r1; s2 > r1; s3 > r1; s4 > r1; s5 > r1; .
. .
According the second strategy, we have:
s1 > r1; s2 > r1; s3 > r1; s4 > r1; s5 > r1; . . .
s1 > r2; s2 > r2; s3 > r2; s4 > r2; s5 > r2; . . .
p. 48

We notice that the second strategy produces twice
more preference relations than the first
These preference relations must be compared with the
relevance judgements of the human assessors
The following conclusions were derived:
Both strategies produce preference relations in agreement with
the relevance judgements in roughly 80% of the cases
Similar agreements are observed even if we swap the first and
second results
Similar agreements are observed even if we reverse the order of
the results
p. 49

These results suggest:
The users provide negative feedback on whole result sets (by not
clicking on them)
The users learn with the process and reformulate better queries
on the subsequent iterations
p. 50

Click-based Ranking
Click through information can be used to improve the
ranking
This can be done by learning a modified ranking
function from click-based preferences
One approach is to use support vector machines
(SVMs) to learn the ranking function
p. 52

Click-based Ranking
In this case, preference relations are transformed into
inequalities among weighted term vectors representing
the ranked documents
These inequalities are then translated into an SVM
optimization problem
The solution of this optimization problem is the optimal
weights for the document terms
The approach proposes the combination of different
retrieval functions with different weights
p. 53

Implicit Feedback Through Local Analysis
p. 54

Local analysis
Local analysis consists in deriving feedback information
from the documents retrieved for a given query q
This is similar to a relevance feedback cycle but done
without assistance from the user
Two local strategies are discussed here: local
clustering and local context analysis
p. 55

Local Clustering
Adoption of clustering techniques for query expansion
has been a basic approach in information retrieval
The standard procedure is to quantify term correlations
and then use the correlated terms for query expansion
Term correlations can be quantified by using global
structures, such as association matrices
However, global structures might not adapt well to the
local context defined by the current query
To deal with this problem, local clustering can be
used, as we now discuss
p. 57

Association Clusters
For a given query q, let
DA: local document set, i.e., set of documents retrieved by q
NA: number of documents in D5
V5: local vocabulary, i.e., set of all distinct words in D5
fi , j : frequency of occurrence of a term ki in a document dj
∈ D5
MA=[mij ]: term-document matrix with V5 rows and N5
columns
mi j =fi , j : an element of matrix MA
MT : transpose of MA
A
The matrix
Cl = Ml MT
p. 58
l
is a local term-term correlation
matrix

Each element cu,v ∈ Cl expresses a
correlation
between terms ku and kv
This relationship between the terms is based on their
joint co-occurrences inside documents of the collection
Higher the number of documents in which the two terms
co-occur, stronger is this correlation
Correlation strengths can be used to define local
clusters of neighbor terms
Terms in a same cluster can then be used for query
expansion
We consider three types of clusters here: association
clusters, metric clusters, and scalar clusters.
p. 59

cu,v =
An association cluster is computed from a local
correlation matrix Cl
For that, we re-define the correlation factors cu,v
between any pair of terms ku and kv, as
follows:
Σ
dj ∈Dl
u,j
f × f v,j
In this case the correlation matrix is referred to as a
local association matrix
The motivation is that terms that co-occur frequently
inside documents have a synonymity association
p. 60

The correlation factors cu,v and the association matrix
Cl are said to be unnormalized
An alternative is to normalize the correlation factors:
c'u,v = cu,v
cu,u + cv,v − cu,v
In this case the association matrix Cl is said to be
normalized
p. 61

Given a local association matrix Cl , we can use it to
build local association clusters as follows
Let Cu(n) be a function that returns the n largest
factors
cu,v ∈ Cl , where v varies over the set of local terms and
v /= u
Then, Cu(n) defines a local association cluster, a
neighborhood, around the term ku
Given a query q, we are normally interested in finding
clusters only for the |q| query terms
This means that such clusters can be computed
efficiently at query time
p. 62

Metric Clusters
Association clusters do not take into account where the
terms occur in a document
However, two terms that occur in a same sentence tend
to be more correlated
A metric cluster re-defines the correlation factors cu,v
as a function of their distances in documents
p. 63

Metric Clusters
Let ku(n, j) be a function that returns the nth
occurrence of term ku in document dj
Further, let r(ku(n, j), kv(m, j)) be a function
that computes the distance between
the nth occurrence of term ku in document dj ; and
the mth occurrence of term kv in document dj
We define,
cu,v =
Σ Σ Σ
dj ∈Dl n m
1
r(ku(n, j), kv(m,
j))
In this case the correlation matrix is referred to as a
local metric matrix
p. 64

Metric Clusters
Notice that if ku and kv are in distinct documents we
take their distance to be infinity
Variations of the above expression for cu,v have been
reported in the literature, such as 1/r2(ku(n, j), kv (m,
j))
The metric correlation factor cu,v quantifies absolute
inverse distances and is said to be unnormalized
Thus, the local metric matrix Cl is said to be
unnormalized
p. 65

Metric Clusters
An alternative is to normalize the correlation factor
For instance,
c'u,v = cu,v
total number of [ku, kv ] pairs
considered
In this case the local metric matrix Cl is said to be
normalized
p. 66

Scalar Clusters
The correlation between two local terms can also be
defined by comparing the neighborhoods of the two
terms
The idea is that two terms with similar
neighborhoods
have some synonymity relationship
In this case we say that the relationship is indirect or induced by
the neighborhood
We can quantify this relationship comparing the neighborhoods of
the terms through a scalar measure
For instance, the cosine of the angle between the two vectors is a
popular scalar similarity measure
p. 67

Scalar Clusters
Let
→su = (cu,x1 , su , x 2 , . . . , su , x n ): vector of neighborhood
correlation values for the term ku
→sv = (cv,y1 , cv,y2 , . . . , cv, y m ): vector of neighborhood
correlation values for term kv
Define,
cu,v =
→su ·
→sv
|→su | ×
|→sv |
In this case the correlation matrix Cl is referred to as a
local scalar matrix
p. 68

Scalar Clusters
The local scalar matrix Cl is said to be induced by the
neighborhood
Let Cu(n) be a function that returns the n largest cu,v
values in a local scalar matrix Cl , v /= u
Then, Cu(n) defines a scalar cluster around term ku
p. 69

Neighbor Terms
Terms that belong to clusters associated to the query
terms can be used to expand the original query
Such terms are called neighbors of the query terms and
are characterized as follows
A term kv that belongs to a cluster Cu(n), associated
with another term ku, is said to be a neighbor of ku
Often, neighbor terms represent distinct keywords that
are correlated by the current query context
p. 70

Neighbor Terms
Consider the problem of expanding a given user query
q
with neighbor terms
One possibility is to expand the query as follows
For each term ku ∈ q, select m neighbor terms from the
cluster Cu(n) and add them to the query
This can be expressed as follows:
qm = q ∪ {kv|kv ∈ Cu(n), ku ∈ q}
Hopefully, the additional neighbor terms kv will retrieve
new relevant documents
p. 71

Neighbor Terms
The set Cu(n) might be composed of terms obtained
using correlation factors normalized and unnormalized
Query expansion is important because it tends to
improve recall
However, the larger number of documents to rank also
tends to lower precision
Thus, query expansion needs to be exercised with great
care and fine tuned for the collection at hand
p. 72

Local Context Analysis
The local clustering techniques are based on the set of
documents retrieved for a query
A distinct approach is to search for term correlations in
the whole collection
Global techniques usually involve the building of a
thesaurus that encodes term relationships in the whole
collection
The terms are treated as concepts and the thesaurus is
viewed as a concept relationship structure
The building of a thesaurus usually considers the use of
small contexts and phrase structures
p. 74

Local context analysis is an approach that combines
global and local analysis
It is based on the use of noun groups, i.e., a single
noun, two nouns, or three adjacent nouns in the text
Noun groups selected from the top ranked documents
are treated as document concepts
However, instead of documents, passages are used for
determining term co-occurrences
Passages are text windows of fixed size
p. 75

More specifically, the local context analysis procedure
operates in three steps
First, retrieve the top n ranked passages using the original
query
Second, for each concept c in the passages compute the
similarity sim(q, c) between the whole query q and the concept
c
Third, the top m ranked concepts, according to sim(q, c),
are added to the original query q
A weight computed as 1 − 0.9 × i/m is assigned to
each concept c, where
i: position of c in the concept ranking
m: number of concepts to add to q
The terms in the original query q might be stressed by
p. 76

Of these three steps, the second one is the most
complex and the one which we now discuss
The similarity sim(q, c) between each concept c and
the original query q is computed as follows
ki∈q
sim(q, c) =
Q
δ
+
i c
log(f
(c,k )×idf )
log n
idfi
where n is the number of top ranked passages
considered
p. 77

The function f (c, ki) quantifies the correlation
between the concept c and the query term ki and is
given by
i
f (c, k )
=
n
Σ
i,j
pf × pf c,j
j=1
where
pfi , j is the frequency of term ki in the j-th passage; and
pfc , j is the frequency of the concept c in the j-th passage
Notice that this is the correlation measure defined for
association clusters, but adapted for passages
p. 78

The inverse document frequency factors are computed
as
idfi
=
idfc
=
5
log10 N/npi
max(1,
)
5
log10 N/npc
max(1,
)
where
N is the number of passages in the collection
npi is the number of passages containing the term ki ; and
npc is the number of passages containing the concept c
The idfi factor in the exponent is introduced to
emphasize infrequent query terms
p. 79

The procedure above for computing sim(q, c) is
a non-trivial variant of tf-idf ranking
It has been adjusted for operation with TREC data and
did not work so well with a different collection
Thus, it is important to have in mind that tuning might
be required for operation with a different collection
p. 80

Implicit Feedback Through Global Analysis
p. 81

Global Context Analysis
The methods of local analysis extract information from
the local set of documents retrieved to expand the
query
An alternative approach is to expand the query using
information from the whole set of documents—a
strategy usually referred to as global analysis
procedures
We distinguish two global analysis procedures:
Query expansion based on a similarity thesaurus
Query expansion based on a statistical thesaurus
p. 82

Query Expansion based on a Similarity
Thesaurus
p. 83

Similarity Thesaurus
We now discuss a query expansion model based on a
global similarity thesaurus constructed automatically
The similarity thesaurus is based on term to term
relationships rather than on a matrix of co-occurrence
Special attention is paid to the selection of terms for
expansion and to the reweighting of these terms
Terms for expansion are selected based on their
similarity to the whole query
p. 84

A similarity thesaurus is built using term to term
relationships
These relationships are derived by considering that the
terms are concepts in a concept space
In this concept space, each term is indexed by the
documents in which it appears
Thus, terms assume the original role of documents
while documents are interpreted as indexing elements
p. 85

Let,
t: number of terms in the collection
N : number of documents in the collection
fi , j : frequency of term ki in document dj
tj : number of distinct index terms in document dj
Then,
t
itfj = log
t
p. 86
j
is the inverse term frequency for
document dj
(analogous to inverse document
frequency)

Within this framework, with each term ki is associated a
vector →ki given by
→ki = (wi,1, wi,2, . . . , wi,N )
These weights are computed as follows
i,j
w
=
(0.5+0.5 f i , j
m a x j ( f i , j )
) itfj
r
Σ N
l=1 (0.5+0.5 f i ,l
ma x l ( fi , l ) )2 itf 2
j
where maxj (fi , j ) computes the maximum of all fi , j
factors for the i-th term
p. 87

The relationship between two terms ku and kv is
computed as a correlation factor cu,v given by
c = k
→
→
u,v u v
Σ
6 dj
u,j
· k = w × w v,j
The global similarity thesaurus is given by the scalar
term-term matrix composed of correlation factors cu,v
This global similarity thesaurus has to be computed
only once and can be updated incrementally
p. 88

Given the global similarity thesaurus, query expansion
is done in three steps as follows
First, represent the query in the same vector space used for
representing the index terms
Second, compute a similarity sim(q, kv ) between each term
kv
correlated to the query terms and the whole query q
Third, expand the query with the top r ranked terms
according to
sim(q, kv )
p. 89

For the first step, the query is represented by a vector
→q given by
Σ
→
→q = w k
i,q i
ki∈q
where wi,q is a term-query weight computed using the
equation for wi,j , but with →q in place of d→j
For the second step, the similarity sim(q, kv)
is computed as
→
p. 90
v v
sim(q, k ) = →q · k
=
Σ
ki∈q
i,q
w × ci,v

A term kv might be closer to the whole query centroid
qC than to the individual query terms
Thus, terms selected here might be distinct from those
selected by previous global analysis methods
p. 91

For the third step, the top r ranked terms are added to
the query q to form the expanded query qm
To each expansion term kv in query qm is assigned a
weight wv,qm given by
wv,qm
sim(q,
kv )
= Σ
ki∈q wi,q
The expanded query qm is then used to retrieve new
documents
This technique has yielded improved retrieval
performance (in the range of 20%) with three different
collections
p. 92

Consider a document dj which is represented in the
→
term vector space by dj =
Σ
k ∈d
i j wi,j→
ki
Assume that the query q is expanded to include all the t
index terms (properly weighted) in the collection
Then, the similarity sim(q, dj ) between dj and q can
be computed in the term vector space by
sim(q, dj ) α
Σ
k v ∈dj
Σ
k u ∈ q wv,j × wu,q × cu,v
p. 93

The previous expression is analogous to the similarity
formula in the generalized vector space model
Thus, the generalized vector space model can be
interpreted as a query expansion technique
The two main differences are
the weights are computed differently
only the top r ranked terms are used
p. 94

Query Expansion based on a Statistical
Thesaurus
p. 95

Global Statistical Thesaurus
We now discuss a query expansion technique based on
a global statistical thesaurus
The approach is quite distinct from the one based on a
similarity thesaurus
The global thesaurus is composed of classes that group
correlated terms in the context of the whole collection
Such correlated terms can then be used to expand the
original user query
p. 96

To be effective, the terms selected for expansion must
have high term discrimination values
This implies that they must be low frequency terms
However, it is difficult to cluster low frequency terms
due to the small amount of information about them
To circumvent this problem, documents are clustered
into classes
The low frequency terms in these documents are then
used to define thesaurus classes
p. 97

A document clustering algorithm that produces small
and tight clusters is the complete link algorithm:
1. Initially, place each document in a distinct cluster
2. Compute the similarity between all pairs of clusters
3. Determine the pair of clusters [Cu, Cv ] with the
highest inter-cluster similarity
4. Merge the clusters Cu and Cv
5. Verify a stop criterion (if this criterion is not met then go back to
step 2)
6. Return a hierarchy of clusters
p. 98

The similarity between two clusters is defined as the
minimum of the similarities between two documents not
in the same cluster
To compute the similarity between documents in a pair,
the cosine formula of the vector model is used
As a result of this minimality criterion, the resultant
clusters tend to be small and tight
p. 99

Cu Cv
Cz
Consider that the whole document collection has been
clustered using the complete link algorithm
Figure below illustrates a portion of the whole cluster
hierarchy generated by the complete link algorithm
0.11
p. 100
0.15
where the inter-cluster similarities are shown in the
ovals

The terms that compose each class of the global
thesaurus are selected as follows
Obtain from the user three parameters:
TC: threshold class
NDC: number of documents in a class
MIDF: minimum inverse document frequency
Paramenter TC determines the document clusters that
will be used to generate thesaurus classes
Two clusters Cu and Cv are selected, when TC is surpassed by
sim(Cu , Cv)
p. 101

Use NDC as a limit on the number of documents of the
clusters
For instance, if both Cu +v and Cu +v + z are selected then the
parameter NDC might be used to decide between the two
MIDF defines the minimum value of IDF for any term
which is selected to participate in a thesaurus class
p. 102

Given that the thesaurus classes have been built, they
can be used for query expansion
For this, an average term weight wtC for each thesaurus
class C is computed as follows
Σ |C|
wtC = i=1
wi,C
|
C|
where
|C| is the number of terms in the thesaurus class C, and
wi , C is a weight associated with the term-class pair [ki,
C]
p. 103

This average term weight can then be used to compute
a thesaurus class weight wC as
C
|
C|
wtC
w = × 0.5
The above weight formulations have been verified
through experimentation and have yielded good results
p. 104

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