Polyrepresentation in a Quantum-inspired Information Retrieval Framework

Polyrepresentation in a Quantum-inspired
Information Retrieval Framework
Ingo Frommholz
@iFromm
University of Bedfordshire
Luton, UK
QUARTZ Winter School
University of Padua

Table of Contents
1 The Principle of Polyrepresentation
2 A Model for Quantum-inspired Information Access
3 Polyrepresentation in a Quantum-inspired IA Model
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The Principle of Polyrepresentation
Cognitive Information Concept in Information Seeking and
Retrieval
Book Store Example
Different Kinds of Polyrepresentation
Retrieval with Polyrepresentation
Polyrepresentative Clustering

Cognitive Information Concept in Information Seeking and Retrieval
Cognitive Communication System
The “Cognitive Freefall”
isfy two conditions simultaneously (Ingwersen 1992, p. 33):
On the one hand information being something which is the
result of a transformation of a generator’s knowledge structures
(by intentionality, model of recipients’ states of knowledge, and in the
form of signs)
and on the other hand being something which,
when perceived, affects and transforms the recipient’s state of knowl-
edge.ee
Recipient World Model
World Model Problem
Space
State of
Uncertainty
Current
Cognitive-
Emotional
State
Perceived objectSignsSigns
InformationInformation
Context B
situation
Context A
situation
TransformationTransformation
InteractionInteraction
Cognitive
free
fall
InformationInformationInformation
processing
gstagesg
Interpretation
Cognitive-EmotionalCognitive-Emotional
Level of SystemLevel of System
Linguistic Level of SystemLinguistic Level of System
Generated object
Generator
Fig. 2.1. The cognitive communication system for Information Science, information
seeking and IR. Revision of Ingwersen (1992, p.33; 1996, p.6), from Belkin (1978).
Evidently, any transformation of state of knowledge involves an effect on
[Ingwersen and Järvelin, 2005, p. 33]
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[Ingwersen, 1994, Ingwersen, 1996, Ingwersen and Järvelin, 2005]
Multi-evidence
Employs the diversity of (cognitively) different actors’
pre-suppositions and interpretations of their situations and
objects over time
Diversity may be derived from same actor but being of different
functional nature (functionally different)
Tries to mitigate the cognitive freefall
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Polyrepresentation
Hypothesis [Ingwersen and Järvelin, 2005, p. 208]
the more interpretations of different cognitive and functional
nature, based on an IS&R situation, that point to a set of
objects in so-called cognitive overlaps, and the more
intensely they do so, the higher the probability that such
objects are relevant (pertinent, useful) to a perceived work
task/interest to be solved, the information (need) situation at
hand, the topic required, or/and the inﬂuencing context of
that situation
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Book Store Example
Motivating Example: Book Store
“Good introduction to quantum mechanics”
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Book Store Example
Motivating Example: Book Store
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Book Store Example
IN Facets and Polyrepresentation
Relevance decision goes beyond topicality
Collections like Amazon/LT/BritishLibrary
Rich pool of potentially useful information (metadata,
user-generated content)
Different views on documents, relevant for different aspects of the
information need (IN)
Combine the evidence (e.g. metadata and user-generated
content) to get a more accurate estimation of
relevance/usefulness
[Koolen, 2014] puts user-generated content into the index – it
worked!
Reviews and tags complimentary to each other and to
professional metadata
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Document/information object polyrepresentation
Information need (IN) polyreprepresentation
Algorithm polyrepresentation
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Document Polyrepresentation
Different document features or properties
Examples
POLAR for annotation-based retrieval
[Frommholz and Fuhr, 2006]
?- document(D) & D[ quantum & mechanics & @A] &
A[ good & introduction ]
Polyrepresentation and CQQL for interactive multimedia IR
[Zellhöfer and Schmitt, 2011]
Features from a query-by-example document interpreted as
representations, translation into CQQL queries
Inter- and intra-document features in polyrepresentation
[Skov et al., 2008]
Cystic Fibrosis test collection: functionally different features: titles,
abstract, references (representing the author); Medical Subject
Headings (MeSH) (representing the indexer as a cognitively
different actor)
Overlaps generated by three or four representations have higher
precision than those generated from two overlaps
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Information Need Polyrepresentation
Perceived work task, problem or information need
Query
Example [Kelly and Fu, 2007]:
What users already know, why they want to know it, TREC
title+description
Additional terms elicited from users used for query expansion
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Algorithm Polyrepresentation
Different weighting schemes
Different relevance feedback and/or query modification algorithms
Example [Larsen et al., 2009]:
4 best performing TREC 5 ad hoc track models over 30 topics
Vogt and Cottrell concluded that not all fusions may outper-
form their individual components; only when almost equally
well-performing retrieval models are fused may the fusion (in
pairs) improve retrieval performance over the constituents.
They regarded the TREC relevance pooling methods as a
large-scale data fusion for IR. Ng and Kantor (2000) applied
TREC 5 routing data, andWu and McClean (2006) made pre-
dictions by means of overlap correlation measures. Ng and
Kantor’s experiments investigated the predictive power of
output dissimilarity and a pairwise measure of similarity of
performance in symmetrical data fusion (p. 1177). Wu and
McClean’s study demonstrated that versions of the same
IR model have a very high overlap correlation and thus
retrieve almost the same documents—a case to be avoided
because nonrelevant documents then tend to be promoted
in line with relevant ones. This view somehow contradicts
the Lee’s findings, but his tests involved different retrieval
models. In summary, there seems to be a consensus that
all the fused IR models should perform equally well. In
pairwise data fusions, the CombMNZ work quite well and
are commonly used, with the CombSUM of retrieval scores
performing nearly as well. When random combinations are
tested, results are mixed concerning which technique to use.
Normalization of retrieval scores should be applied, and if
not feasible, the Borda solution where rank scores are used
seems to perform well.
Most data fusion experiments in IR, including the ones
presented here, are based on retrieval results from already
performed searches in TREC. The analysis or prediction
methodologies in the present study are associated with
the principle of polyrepresentation. The difference lies in the
approach to prediction. While the former methodologies
attempt to make predictions based on automated and quan-
titative perspectives of the overlaps, our approach is from
a qualitative and conceptual/algorithmic perspective. In a
polyrepresentation sense, the more evidence deriving from
qualitatively different sources that point to a document, the
higher the probability that that document is (highly) rele-
vant. Thus, the relative size of overlap between fused IR
models has a quite different meaning in polyrepresentation.
In data fusion based on polyrepresentation, there are fun-
damentally two ways of combining retrieval systems. One
way is the restricted overlap fusion. Following this method,
only the inner (disjoint) overlap of the fused models provides
the result set to be ranked. Figure 1 illustrates this exper-
imental situation with four different retrieval models—and
their triple and pairwise disjoint overlaps as well as their
inner “central cognitive overlap” formed by all four models
(Fuse4). As the sets are disjoint, each of the 11 overlapping
sets constitutes separate data fusion results, and the perfor-
mance of each can be studied. Note that in the restricted
fusion, each single original retrieval model only includes the
documents that are “leftover;” that is, they do not include any
of the documents in overlaps with other retrieval models. For
instance,theperformanceoftheoriginalretrievalmodelCOR
is thus measured on the documents found in COR oval (1)
but not including the already retrieved documents in Fuse2
to Fuse4 areas (white area, Figure 1). Their performance
FIG. 1. Illustration of polyrepresentation of four different retrieval models’
search results in the form of disjoint overlapping documents (variation of
Ingwersen & Järvelin, 2005, p. 347; Lund, Schneider, & Ingwersen, 2006).
648 JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE AND TECHNOLOGY—April 2009
DOI: 10.1002/asi
Restricted fusions made of two, three, or four
cognitively/algorithmically very different retrieval models perform
significantly better than the individual models
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1 Get ranking for different representations
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2 Find the cognitive overlap
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Polyrepresentation
Book Store Scenario
Content Author
Ratings
Comments
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Polyrepresentation and Clustering
Polyrepresentation creates
partitions
Clustering partitions
document sets too
Can clustering help in
creating polyrepresentative
partitions?
Polyrepresentation Cluster
Hypothesis: “documents
relevant to the same
representations should
appear in the same clus-
ter” [Frommholz and Abbasi, 2014]
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Polyrepresentation and Clustering
Mapping of clusters to
polyrepresentation (using
iSearch [Lykke et al., 2010])
Simulated user – search
strategy:
1 User investigates total
cognitive overlap cluster
2 User jumps to different
cluster based on
preferences
3 The user simulation
creates a ranked list of
documents
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Information Need-based Vector
Let REPin be the set of representations1
of an information need in
Motivated by the Optimum Clustering Framework (OCF), which is
based on the probability of relevance [Fuhr et al., 2011]
Pr(R|d,ri ) is computed for each document d and ri ∈ REPin
τin(d) =


Pr(R|d,r1)
...
Pr(R|d,rn)

 (1)
1
search terms, work task, ideal answer, current info need, background knowledge
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Document-based Polyrepresentation Vector
REPd consists of the different representations2
rdi of a document
d
Pr(R|rdi ,q) for q (search terms in this case) is computed
τdoc(d) =


Pr(R|rd1,q)
...
Pr(R|rdn,q)

 (2)
2
title, abstract, body, bibliographic context, references
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Some Findings (using iSearch)
Some statistically significant improvements over a BM25 baseline
(NDCG@30) using the ranking created by a simple simulated
user strategy when concatenating the IN and Document
representations [Abbasi and Frommholz, 2015b]
Statistical significant improvements (NDCG) when using
document and IN representations separately and assuming an
ideal (oracle-based) cluster ranking
[Abbasi and Frommholz, 2015a]
This shows us our idea is basically promising!
Finding the total cognitve overlap (TOC) using cluster ranking is
challenging [Frommholz and Abbasi, 2014]
Different interpretations of the TOC: The one with the highest
precision? The one with the highest pairwise precision? The one
where all representations get a high value?
The latter one could be identified more easily (MRR = 0.575
compared to around 0.3 for the others)
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A Model for Quantum-inspired
Information Access
Quantum Information Access
Information Need Space
User Interaction and Feedback
Textual Representation
Evaluation
QIA Conclusion

Quantum Information Access
Assumptions underlying QIA
IR system uncertain about user’s information need (IN)
System view of the user’s IN becomes more and more speciﬁc
through interaction
The IN may change from the user’s point of view
There is an IN Space, a Hilbert space
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|quantum mechanics
INs as vectors: IN
vector |φ〉
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R
|quantum mechanics
INs as vectors: IN
vector |φ〉
Event “document d is
relevant” represented
by subspace R
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R
|quantum mechanics
INs as vectors: IN
vector |φ〉
Event “document d is
relevant” represented
by subspace R
Probability of
relevance: squared
length of projection
Pr(R|d,φ) =
||R |φ〉||2
Unit vector imposes
relevance distribution
on subspaces (events)
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System’s Uncertainty about User’s Intentions
R
p1
p2
p4
p3
p5
System uncertain about
user’s IN
Expressed by an ensemble S
of possible IN vectors (density
ρ):
S = {(p1,|φ1〉),...,(pn,|φn〉)}
Probability of relevance:
Pr(R|d,S)=
i
pi ·Pr(R|d,φi )
=||R|φ〉||2
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System’s Uncertainty about User’s Intentions
R
p1
p2
p4
p3
p5
Dual representation using
density operator and trace
function
ρ = i pi ·|φi 〉〈φi |
Pr(R|d,S) = tr(ρR)
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R∗
|ϕ1
|ϕ2
|ϕ5
|ϕ3
Outcome of feedback: Query
and query reformulation, (click
on) relevant document, ...
Expressed as subspace
Project IN vectors onto
document subspace
Document now gets
probability 1
System’s uncertainty
decreases
Also reﬂects changes in
information needs
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R∗
|ϕ1
|ϕ2
|ϕ4
|ϕ3
|ϕ5
Outcome of feedback: Query
and query reformulation, (click
on) relevant document, ...
Expressed as subspace
Project IN vectors onto
document subspace
Document now gets
probability 1
System’s uncertainty
decreases
Also reﬂects changes in
information needs
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IN Space / Documents
|crash (Term)
|car (Term)
|jupiter (Term)
|jupiter crash
|car crash
|ϕ
IN space based on term
space
IN vectors made of document
fragments
Weighting scheme (e.g., tf,
tf-idf,...)
Document is relevant to all
INs found in its fragments
Document subspace R
spanned by IN vectors
No length normalisation
necessary
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Single Query Term
Take all fragments vectors (IN
vectors) containing term t
This makes up ensemble St
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Mixture
Mixture of all combinations of
term fragments
Document must at least
satisfy one term fragment
The more term fragments are
contained, the more relevant
a document is
S(M) =
n
i=1
wi Sti
wi is term weight
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Mixture of Superposition
Superpose all combinations
(e.g.
1
2
(|φ〉+|ψ〉))
At least one query term
fragment superposition must
be contained
The more fragment
superpositions are contained,
the more relevant a document
is
Indication that it works well
with multi-term concepts (e.g.
“digital libraries”)
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Tensor product
Assumption: each term
covers an IN aspect
Tensor product of all fragment
vectors combination of IN
aspects
Document must satisfy all IN
aspects
The more tensor products are
satisﬁed, the more relevant is
the document
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Evaluation
Evaluation
Evaluation with several TREC collections
[Piwowarski et al., 2010]
Tensor representation of query could compete with BM25
We don’t lose retrieval effectiveness in an ad hoc scenario
Expressive framework
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QIA Conclusion
QIA Extensions
What can it bring to IR?
Queries in sessions [Frommholz et al., 2011]
Use geometry and projections to determine type of and handle
follow-up query (generalisation, information need drift,
specialisation)
Different forms of interactions (query reformulations, relevance
judgements)
Summarisation [Piwowarski et al., 2012]
QIA interpretation of LSA-based methods
Query algebra for the QIA framework [Caputo et al., 2011]
Diversity and novelty
Polyrepresentation (next)
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QIA Conclusion
QIA Conclusion
User’s IN as ensemble of vectors
Documents as subspaces
User interaction and feedback
Term space, query construction
Can compete in an ad hoc scenario
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Polyrepresentation in a
Quantum-inspired IA Model
Modelling Polyprepresentation
Combining the evidence
Relationships between representations

Polyrepresentation in a Quantum-inspired IA Model
Book Store Scenario
Content Author
Ratings
Comments
2 Find the cognitive overlap
Based on different document representations, but also different
representations of user’s information need
Hypothesis: cognitive overlap contains highly relevant documents
(experiments support this)
43 / 70

How can we apply this in QIA?
Model single representations in a vector space (by example)
Authors
Ratings
Topical/term space: already discussed
Combine the representations
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Example: Author Space
Each author is a dimension
Non-orthogonal vectors:
dependencies
Angle between vectors
reﬂects the degree of
dependency (90◦ =
orthogonal = upright =
independent)
Example: Jones and Smith
(somehow) related, Smith and
Miller not
45 / 70

Example: Author Space
Document by Smith and Miller
User seeks for documents by
Jones
Document retrieved due to
relationship between Jones
and Smith
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Author/Topic Space
Combined author/topic space
Authors may be related only
w.r.t. a speciﬁc topic
Ex.: A user interested in
Smith’ documents about
logics may be interested in
Jones’ documents about
logics, but not in Jones’
documents about interactive
IR
Author represented as a
subspace
|SmithLogics
|JonesLogics
|JonesIIR
47 / 70

Rating Space
Example: rating scale
good/bad/average – each is a
dimension
“Average” rated book
represented by 2-dimensional
subspace
User wants books which are
rated good
⇒ not relevant (|good〉
orthogonal)
Rrating
|good
|average
|bad
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Combining the Evidence
Total Cognitive Overlap and Tensors
Content Author
Ratings
Comments
Modelled different representations in vector space
Probabilities w.r.t. single representations
How do we express user’s IN w.r.t. all representations?
How do we get a cognitive overlap?
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Combining the Evidence
Total Cognitive Overlap and Tensors
Content Author
Ratings
Comments
Polyrepresentation space as tensor product (“⊗”) of single
spaces
Probability that document is in total cognitive overlap:
Prpolyrep = Prcontent ·Prratings ·Prauthor ·Prcomments
50 / 70

Wishlist
Content Author
Ratings
Comments
Documents not relevant in one representation should not get a
value of 0
Ignore selected representations
Relative importance of representations to user (mixing and
weighting)
51 / 70

“Don’t care” dimension
Introduction of a “don’t care” dimension
Part of each document subspace
each document “satisﬁes” the don’t care “need”
Example: Document by Smith, user doesn’t care about authors
with probability α
|smith
|jones
|∗
α
Rauthor
α = 1 means representation is ignored at all
52 / 70

Example
What the system assumes about the user’s IN:
Seeks books either by Jones or by Smith
Looks either for good books or doesn’t care about ratings
Assume a document d by Smith which is rated “bad”
Polyrepresentation space: 9-dimensional (3× 3)
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Documents in Polyrepresentation Space
Represented as tensor product of single document subspaces
Here: 4-dimensional subspace (2× 2)
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Determining the Retrieval Weight
Why the system retrieves the
bad book by Smith
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Determining the Retrieval Weight
Why the system retrieves the
bad book by Smith
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Something left on the Wishlist
Relationships between Representations
System observes (interaction/feedback) user preferences:
If book is by Smith, it has to be rated good
If book is by Jones, don’t care about the ratings
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Something left on the Wishlist
Relationships between Representations
System observes (interaction/feedback) user preferences:
If book is by Smith, it has to be rated good
If book is by Jones, don’t care about the ratings
System evolves to new state in polyrepresentation space (2
combinations not allowed any more)
X
X
59 / 70

What does that mean?
Only two assumed IN
cases left:
1 Smith/good
2 Jones/don’t care
Cannot be expressed as
combination of single
representations
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What does that mean?
Only two assumed IN
cases left:
1 Smith/good
2 Jones/don’t care
Cannot be expressed as
combination of single
representations
Bad book by Smith only
retrieved due to
relationship to Jones!
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Polyrepresentation Conclusion
Different non-topical representations as subspaces
Polyrepresentation space as tensor space to calculate cognitive
overlap
“Don’t care” dimension for weighting of representations
Non-separate states
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Bibliography
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