Data Mining

Classification and
Prediction
What is classification? What is prediction?
Issues regarding classification and prediction
Classification by decision tree induction
Bayesian Classification
Classification by backpropagation
Classification based on concepts from association rule
mining
Other Classification Methods
Prediction
Classification accuracy
Summary

Classification:
predicts categorical class labels
classifies data (constructs a model) based on the
training set and the values (class labels) in a
classifying attribute and uses it in classifying new data
Prediction:
models continuous-valued functions, i.e., predicts
unknown or missing values
Typical Applications
credit approval
target marketing
medical diagnosis
treatment effectiveness analysis
Classification vs.
Prediction

Classification—A Two-Step
Process
Model construction: describing a set of predetermined
classes
Each tuple/sample is assumed to belong to a predefined class,
as determined by the class label attribute
The set of tuples used for model construction: training set
The model is represented as classification rules, decision trees,
or mathematical formulae
Model usage: for classifying future or unknown objects
Estimate accuracy of the model
The known label of test sample is compared with the
classified result from the model
Accuracy rate is the percentage of test set samples that are
correctly classified by the model
Test set is independent of training set, otherwise over-fitting
will occur

Classification Process
(1): Model Construction
Training
Data
NAME RANK YEARS TENURED
Mike Assistant Prof 3 no
Mary Assistant Prof 7 yes
Bill Professor 2 yes
Jim Associate Prof 7 yes
Dave Assistant Prof 6 no
Anne Associate Prof 3 no
Classification
Algorithms
IF rank = ‘professor’
OR years > 6
THEN tenured = ‘yes’
Classifier
(Model)

Classification Process (2): Use
the Model in Prediction
Classifier
Testing
Data
NAME RANK YEARS TENURED
Tom Assistant Prof 2 no
Merlisa Associate Prof 7 no
George Professor 5 yes
Joseph Assistant Prof 7 yes
Unseen Data
(Jeff, Professor, 4)
Tenured?

Supervised vs.
Unsupervised Learning
Supervised learning (classification)
Supervision: The training data (observations,
measurements, etc.) are accompanied by labels
indicating the class of the observations
New data is classified based on the training set
Unsupervised learning (clustering)
The class labels of training data is unknown
Given a set of measurements, observations, etc. with
the aim of establishing the existence of classes or
clusters in the data

Issues (1): Data Preparation
Data cleaning
Preprocess data in order to reduce noise and handle
missing values
Relevance analysis (feature selection)
Remove the irrelevant or redundant attributes
Data transformation
Generalize and/or normalize data

Issues (2): Evaluating
Classification Methods
Predictive accuracy
Speed and scalability
time to construct the model
time to use the model
Robustness
handling noise and missing values
Scalability
efficiency in disk-resident databases
Interpretability:
understanding and insight provded by the model
Goodness of rules
decision tree size
compactness of classification rules

Classification by Decision
Tree Induction
Decision tree
A flow-chart-like tree structure
Internal node denotes a test on an attribute
Branch represents an outcome of the test
Leaf nodes represent class labels or class distribution
Decision tree generation consists of two phases
Tree construction
At start, all the training examples are at the root
Partition examples recursively based on selected attributes
Tree pruning
Identify and remove branches that reflect noise or outliers
Use of decision tree: Classifying an unknown sample
Test the attribute values of the sample against the decision tree

Training Dataset
age income student credit_rating
<=30 high no fair
<=30 high no excellent
31…40 high no fair
>40 medium no fair
>40 low yes fair
>40 low yes excellent
31…40 low yes excellent
<=30 medium no fair
<=30 low yes fair
>40 medium yes fair
<=30 medium yes excellent
31…40 medium no excellent
31…40 high yes fair
>40 medium no excellent
This
follows
an
example
from
Quinlan’s
ID3

Output: A Decision Tree for
“buys_computer”
age?
overcast
student? credit rating?
no yes fairexcellent
<=30 >40
no noyes yes
yes
30..40

Algorithm for Decision
Tree Induction
Basic algorithm (a greedy algorithm)
Tree is constructed in a top-down recursive divide-and-conquer
manner
At start, all the training examples are at the root
Attributes are categorical (if continuous-valued, they are
discretized in advance)
Examples are partitioned recursively based on selected attributes
Test attributes are selected on the basis of a heuristic or statistical
measure (e.g., information gain)
Conditions for stopping partitioning
All samples for a given node belong to the same class
There are no remaining attributes for further partitioning – majority
voting is employed for classifying the leaf
There are no samples left

Attribute Selection
Measure
Information gain (ID3/C4.5)
All attributes are assumed to be categorical
Can be modified for continuous-valued attributes
Gini index (IBM IntelligentMiner)
All attributes are assumed continuous-valued
Assume there exist several possible split values for each
attribute
May need other tools, such as clustering, to get the
possible split values
Can be modified for categorical attributes

Information Gain
(ID3/C4.5)
Select the attribute with the highest information gain
Assume there are two classes, P and N
Let the set of examples S contain p elements of class P
and n elements of class N
The amount of information, needed to decide if an
arbitrary example in S belongs to P or N is defined as
np
n
np
n
np
p
np
p
npI
++
−
++
−= 22 loglog),(

Information Gain in
Decision Tree Induction
Assume that using attribute A a set S will be
partitioned into sets {S1, S2 , …, Sv}
If Si contains pi examples of P and ni examples of N,
the entropy, or the expected information needed to
classify objects in all subtrees Si is
The encoding information that would be gained
by branching on A
∑
= +
+
=
ν
1
),()(
i
ii
ii
npI
np
np
AE
)(),()( AEnpIAGain −=

Attribute Selection by
Information Gain Computation
 Class P: buys_computer
= “yes”
 Class N: buys_computer
= “no”
 I(p, n) = I(9, 5) =0.940
 Compute the entropy for
age:
Hence
Similarly
age pi ni I(pi, ni)
<=30 2 3 0.971
30…40 4 0 0
>40 3 2 0.971
69.0)2,3(
14
5
)0,4(
14
4
)3,2(
14
5
)(
=+
+=
I
IIageE
048.0)_(
151.0)(
029.0)(
=
=
=
ratingcreditGain
studentGain
incomeGain
)(),()( ageEnpIageGain −=

Gini Index (IBM IntelligentMiner)
If a data set T contains examples from n classes, gini index,
gini(T) is defined as
where pj is the relative frequency of class j in T.
If a data set T is split into two subsets T1 and T2 with sizes N1
and N2 respectively, the gini index of the split data contains
examples from n classes, the gini index gini(T) is defined as
The attribute provides the smallest ginisplit(T) is chosen to split
the node (need to enumerate all possible splitting points for
each attribute).
∑
=
−=
n
j
p jTgini
1
21)(
)()()( 2
2
1
1
Tgini
N
N
Tgini
N
NTginisplit
+=

Extracting Classification
Rules from Trees
Represent the knowledge in the form of IF-THEN rules
One rule is created for each path from the root to a leaf
Each attribute-value pair along a path forms a conjunction
The leaf node holds the class prediction
Rules are easier for humans to understand
Example
IF age = “<=30” AND student = “no” THEN buys_computer = “no”
IF age = “<=30” AND student = “yes” THEN buys_computer = “yes”
IF age = “31…40” THEN buys_computer = “yes”
IF age = “>40” AND credit_rating = “excellent” THEN
buys_computer = “yes”
IF age = “>40” AND credit_rating = “fair” THEN buys_computer = “no”

Avoid Overfitting in
Classification
The generated tree may overfit the training data
Too many branches, some may reflect anomalies
due to noise or outliers
Result is in poor accuracy for unseen samples
Two approaches to avoid overfitting
Prepruning: Halt tree construction early—do not split
a node if this would result in the goodness measure
falling below a threshold
Difficult to choose an appropriate threshold
Postpruning: Remove branches from a “fully grown”
tree—get a sequence of progressively pruned trees
Use a set of data different from the training data
to decide which is the “best pruned tree”

Approaches to Determine
the Final Tree Size
Separate training (2/3) and testing (1/3) sets
Use cross validation, e.g., 10-fold cross
validation
Use all the data for training
but apply a statistical test (e.g., chi-square) to
estimate whether expanding or pruning a node
may improve the entire distribution
Use minimum description length (MDL) principle:
halting growth of the tree when the encoding is

Enhancements to basic
decision tree induction
Allow for continuous-valued attributes
Dynamically define new discrete-valued attributes that
partition the continuous attribute value into a discrete
set of intervals
Handle missing attribute values
Assign the most common value of the attribute
Assign probability to each of the possible values
Attribute construction
Create new attributes based on existing ones that are
sparsely represented
This reduces fragmentation, repetition, and replication

Classification in Large
Databases
Classification—a classical problem extensively studied by
statisticians and machine learning researchers
Scalability: Classifying data sets with millions of examples
and hundreds of attributes with reasonable speed
Why decision tree induction in data mining?
relatively faster learning speed (than other classification
methods)
convertible to simple and easy to understand
classification rules
can use SQL queries for accessing databases
comparable classification accuracy with other methods

Scalable Decision Tree Induction
Methods in Data Mining Studies
SLIQ (EDBT’96 — Mehta et al.)
builds an index for each attribute and only class list and
the current attribute list reside in memory
SPRINT (VLDB’96 — J. Shafer et al.)
constructs an attribute list data structure
PUBLIC (VLDB’98 — Rastogi & Shim)
integrates tree splitting and tree pruning: stop growing
the tree earlier
RainForest (VLDB’98 — Gehrke, Ramakrishnan & Ganti)
separates the scalability aspects from the criteria that
determine the quality of the tree
builds an AVC-list (attribute, value, class label)

Data Cube-Based Decision-
Tree Induction
Integration of generalization with decision-tree
induction (Kamber et al’97).
Classification at primitive concept levels
E.g., precise temperature, humidity, outlook, etc.
Low-level concepts, scattered classes, bushy
classification-trees
Semantic interpretation problems.
Cube-based multi-level classification
Relevance analysis at multi-levels.
Information-gain analysis with dimension + level.

Presentation of
Classification Results

Classification and
Prediction
What is classification? What is prediction?
Issues regarding classification and prediction
Classification by decision tree induction
Bayesian Classification
Classification by backpropagation
Classification based on concepts from
association rule mining
Other Classification Methods
Prediction
Classification accuracy
Summary

Bayesian Classification:
Why?
Probabilistic learning: Calculate explicit probabilities for
hypothesis, among the most practical approaches to certain
types of learning problems
Incremental: Each training example can incrementally
increase/decrease the probability that a hypothesis is
correct. Prior knowledge can be combined with observed
data.
Probabilistic prediction: Predict multiple hypotheses,
weighted by their probabilities
Standard: Even when Bayesian methods are
computationally intractable, they can provide a standard of
optimal decision making against which other methods can
be measured

Bayesian Theorem
Given training data D, posteriori probability of a
hypothesis h, P(h|D) follows the Bayes theorem
MAP (maximum posteriori) hypothesis
Practical difficulty: require initial knowledge of
many probabilities, significant computational
cost
)(
)()|()|(
DP
hPhDPDhP =
.)()|(maxarg)|(maxarg hPhDP
Hh
DhP
HhMAP
h
∈
=
∈
≡

Bayesian classification
The classification problem may be formalized
using a-posteriori probabilities:
P(C|X) = prob. that the sample tuple
X=<x1,…,xk> is of class C.
E.g. P(class=N | outlook=sunny,windy=true,…)
Idea: assign to sample X the class label C such
that P(C|X) is maximal

Estimating a-posteriori
probabilities
Bayes theorem:
P(C|X) = P(X|C)·P(C) / P(X)
P(X) is constant for all classes
P(C) = relative freq of class C samples
C such that P(C|X) is maximum =
C such that P(X|C)·P(C) is maximum
Problem: computing P(X|C) is unfeasible!

Naïve Bayesian
Classification
Naïve assumption: attribute independence
P(x1,…,xk|C) = P(x1|C)·…·P(xk|C)
If i-th attribute is categorical:
P(xi|C) is estimated as the relative freq of
samples having value xi as i-th attribute in class
C
If i-th attribute is continuous:
P(xi|C) is estimated thru a Gaussian density
function
Computationally easy in both cases

The independence
hypothesis…
… makes computation possible
… yields optimal classifiers when satisfied
… but is seldom satisfied in practice, as
attributes (variables) are often correlated.
Attempts to overcome this limitation:
Bayesian networks, that combine Bayesian reasoning
with causal relationships between attributes
Decision trees, that reason on one attribute at the
time, considering most important attributes first

Bayesian Belief Networks
(I)
Family
History
LungCancer
PositiveXRay
Smoker
Emphysema
Dyspnea
LC
~LC
(FH, S) (FH, ~S)(~FH, S) (~FH, ~S)
0.8
0.2
0.5
0.5
0.7
0.3
0.1
0.9
The conditional probability table
for the variable LungCancer

(II)
Bayesian belief network allows a subset of the
variables conditionally independent
A graphical model of causal relationships
Several cases of learning Bayesian belief
networks
Given both network structure and all the variables: easy
Given network structure but only some variables
When the network structure is not known in advance

Neural Networks
Advantages
prediction accuracy is generally high
robust, works when training examples contain errors
output may be discrete, real-valued, or a vector of
several discrete or real-valued attributes
fast evaluation of the learned target function
Criticism
long training time
difficult to understand the learned function (weights)
not easy to incorporate domain knowledge

A Neuron
The n-dimensional input vector x is mapped
into variable y by means of the scalar
product and a nonlinear function mapping
µk-
f
weighted
sum
Input
vector x
output y
Activation
function
weight
vector w
∑
w0
w1
wn
x0
x1
xn

Network Training
The ultimate objective of training
obtain a set of weights that makes almost all the
tuples in the training data classified correctly
Steps
Initialize weights with random values
Feed the input tuples into the network one by one
For each unit
Compute the net input to the unit as a linear combination of
all the inputs to the unit
Compute the output value using the activation function
Compute the error
Update the weights and the bias

Multi-Layer Perceptron
Output nodes
Input nodes
Hidden nodes
Output vector
Input vector: xi
wij
∑ +=
i
jiijj OwI θ
jIj
e
O −
+
=
1
1
))(1( jjjjj OTOOErr −−=
jk
k
kjjj wErrOOErr ∑−= )1(
ijijij OErrlww )(+=
jjj Errl)(+=θθ

Association-Based
Classification
Several methods for association-based
classification
ARCS: Quantitative association mining and clustering
of association rules (Lent et al’97)
It beats C4.5 in (mainly) scalability and also accuracy
Associative classification: (Liu et al’98)
It mines high support and high confidence rules in the form of
“cond_set => y”, where y is a class label
CAEP (Classification by aggregating emerging
patterns) (Dong et al’99)
Emerging patterns (EPs): the itemsets whose support
increases significantly from one class to another
Mine Eps based on minimum support and growth rate

Other Classification
Methods
k-nearest neighbor classifier
case-based reasoning
Genetic algorithm
Rough set approach
Fuzzy set approaches

Instance-Based Methods
Instance-based learning:
Store training examples and delay the processing
(“lazy evaluation”) until a new instance must be
classified
Typical approaches
k-nearest neighbor approach
Instances represented as points in a Euclidean
space.
Locally weighted regression
Constructs local approximation
Case-based reasoning
Uses symbolic representations and knowledge-
based inference

The k-Nearest Neighbor
Algorithm
All instances correspond to points in the n-D
space.
The nearest neighbor are defined in terms of
Euclidean distance.
The target function could be discrete- or real-
valued.
For discrete-valued, the k-NN returns the most
common value among the k training examples
nearest to xq.
Vonoroi diagram: the decision surface induced
by 1-NN for a typical set of training examples..
_
+
_ xq
+
_ _
+
_
_
+
.
.
.
. .

Discussion on the k-NN
Algorithm
The k-NN algorithm for continuous-valued target functions
Calculate the mean values of the k nearest neighbors
Distance-weighted nearest neighbor algorithm
Weight the contribution of each of the k neighbors
according to their distance to the query point xq
giving greater weight to closer neighbors
Similarly, for real-valued target functions
Robust to noisy data by averaging k-nearest neighbors
Curse of dimensionality: distance between neighbors could
be dominated by irrelevant attributes.
To overcome it, axes stretch or elimination of the least
relevant attributes.
w
d xq xi
≡ 1
2( , )

Case-Based Reasoning
Also uses: lazy evaluation + analyze similar instances
Difference: Instances are not “points in a Euclidean space”
Example: Water faucet problem in CADET (Sycara et al’92)
Methodology
Instances represented by rich symbolic descriptions
(e.g., function graphs)
Multiple retrieved cases may be combined
Tight coupling between case retrieval, knowledge-based
reasoning, and problem solving
Research issues
Indexing based on syntactic similarity measure, and
when failure, backtracking, and adapting to additional
cases

Remarks on Lazy vs. Eager
Learning
Instance-based learning: lazy evaluation
Decision-tree and Bayesian classification: eager evaluation
Key differences
Lazy method may consider query instance xq when deciding how to
generalize beyond the training data D
Eager method cannot since they have already chosen global
approximation when seeing the query
Efficiency: Lazy - less time training but more time predicting
Accuracy
Lazy method effectively uses a richer hypothesis space since it
uses many local linear functions to form its implicit global
approximation to the target function
Eager: must commit to a single hypothesis that covers the entire
instance space

Genetic Algorithms
GA: based on an analogy to biological evolution
Each rule is represented by a string of bits
An initial population is created consisting of randomly
generated rules
e.g., IF A1 and Not A2 then C2 can be encoded as 100
Based on the notion of survival of the fittest, a new
population is formed to consists of the fittest rules and
their offsprings
The fitness of a rule is represented by its classification
accuracy on a set of training examples
Offsprings are generated by crossover and mutation

Rough Set Approach
Rough sets are used to approximately or “roughly”
define equivalent classes
A rough set for a given class C is approximated by two
sets: a lower approximation (certain to be in C) and an
upper approximation (cannot be described as not
belonging to C)
Finding the minimal subsets (reducts) of attributes (for
feature reduction) is NP-hard but a discernibility matrix
is used to reduce the computation intensity

Fuzzy
Sets
Fuzzy logic uses truth values between 0.0 and 1.0 to
represent the degree of membership (such as using
fuzzy membership graph)
Attribute values are converted to fuzzy values
e.g., income is mapped into the discrete categories
{low, medium, high} with fuzzy values calculated
For a given new sample, more than one fuzzy value may
apply
Each applicable rule contributes a vote for membership
in the categories
Typically, the truth values for each predicted category
are summed

What Is Prediction?
Prediction is similar to classification
First, construct a model
Second, use model to predict unknown value
Major method for prediction is regression
• Linear and multiple regression
• Non-linear regression
Prediction is different from classification
Classification refers to predict categorical class label
Prediction models continuous-valued functions

Predictive modeling: Predict data values or construct
generalized linear models based on the database data.
One can only predict value ranges or category distributions
Method outline:
Minimal generalization
Attribute relevance analysis
Generalized linear model construction
Prediction
Determine the major factors which influence the prediction
Data relevance analysis: uncertainty measurement,
entropy analysis, expert judgement, etc.
Multi-level prediction: drill-down and roll-up analysis
Predictive Modeling in
Databases

Linear regression: Y = α + β X
Two parameters , α and β specify the line and are to
be estimated by using the data at hand.
using the least squares criterion to the known values of
Y1, Y2, …, X1, X2, ….
Multiple regression: Y = b0 + b1 X1 + b2 X2.
Many nonlinear functions can be transformed into the
above.
Log-linear models:
The multi-way table of joint probabilities is
approximated by a product of lower-order tables.
Probability: p(a, b, c, d) = αab βacχad δbcd
Regress Analysis and Log-
Linear Models in Prediction

Classification Accuracy:
Estimating Error Rates
Partition: Training-and-testing
use two independent data sets, e.g., training set (2/3),
test set(1/3)
used for data set with large number of samples
Cross-validation
divide the data set into k subsamples
use k-1 subsamples as training data and one sub-
sample as test data --- k-fold cross-validation
for data set with moderate size
Bootstrapping (leave-one-out)
for small size data

Boosting and Bagging
Boosting increases classification
accuracy
Applicable to decision trees or Bayesian
classifier
Learn a series of classifiers, where
each classifier in the series pays more
attention to the examples misclassified
by its predecessor
Boosting requires only linear time and
constant space

Boosting Technique (II) —
Algorithm
Assign every example an equal weight 1/N
For t = 1, 2, …, T Do
Obtain a hypothesis (classifier) h(t)
under w(t)
Calculate the error of h(t) and re-weight the
examples based on the error
Normalize w(t+1)
to sum to 1
Output a weighted sum of all the hypothesis,
with each hypothesis weighted according to its
accuracy on the training set

Summary
Classification is an extensively studied problem (mainly in
statistics, machine learning & neural networks)
Classification is probably one of the most widely used
data mining techniques with a lot of extensions
Scalability is still an important issue for database
applications: thus combining classification with database
techniques should be a promising topic
Research directions: classification of non-relational data,
e.g., text, spatial, multimedia, etc..

References (I)
C. Apte and S. Weiss. Data mining with decision trees and decision rules. Future
Generation Computer Systems, 13, 1997.
L. Breiman, J. Friedman, R. Olshen, and C. Stone. Classification and Regression Trees.
Wadsworth International Group, 1984.
P. K. Chan and S. J. Stolfo. Learning arbiter and combiner trees from partitioned data for
scaling machine learning. In Proc. 1st Int. Conf. Knowledge Discovery and Data Mining
(KDD'95), pages 39-44, Montreal, Canada, August 1995.
U. M. Fayyad. Branching on attribute values in decision tree generation. In Proc. 1994
AAAI Conf., pages 601-606, AAAI Press, 1994.
J. Gehrke, R. Ramakrishnan, and V. Ganti. Rainforest: A framework for fast decision tree
construction of large datasets. In Proc. 1998 Int. Conf. Very Large Data Bases, pages
416-427, New York, NY, August 1998.
M. Kamber, L. Winstone, W. Gong, S. Cheng, and J. Han. Generalization and decision
tree induction: Efficient classification in data mining. In Proc. 1997 Int. Workshop
Research Issues on Data Engineering (RIDE'97), pages 111-120, Birmingham, England,
April 1997.

References (II)
J. Magidson. The Chaid approach to segmentation modeling: Chi-squared automatic
interaction detection. In R. P. Bagozzi, editor, Advanced Methods of Marketing
Research, pages 118-159. Blackwell Business, Cambridge Massechusetts, 1994.
M. Mehta, R. Agrawal, and J. Rissanen. SLIQ : A fast scalable classifier for data mining.
In Proc. 1996 Int. Conf. Extending Database Technology (EDBT'96), Avignon, France,
March 1996.
S. K. Murthy, Automatic Construction of Decision Trees from Data: A Multi-Diciplinary
Survey, Data Mining and Knowledge Discovery 2(4): 345-389, 1998
J. R. Quinlan. Bagging, boosting, and c4.5. In Proc. 13th Natl. Conf. on Artificial
Intelligence (AAAI'96), 725-730, Portland, OR, Aug. 1996.
R. Rastogi and K. Shim. Public: A decision tree classifer that integrates building and
pruning. In Proc. 1998 Int. Conf. Very Large Data Bases, 404-415, New York, NY,
August 1998.
J. Shafer, R. Agrawal, and M. Mehta. SPRINT : A scalable parallel classifier for data
mining. In Proc. 1996 Int. Conf. Very Large Data Bases, 544-555, Bombay, India, Sept.
1996.
S. M. Weiss and C. A. Kulikowski. Computer Systems that Learn: Classification and
Prediction Methods from Statistics, Neural Nets, Machine Learning, and Expert Systems.
Morgan Kaufman, 1991.

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