Business Systems Intelligence:

5. Classification 1

Dr. B

rian Mac N

amee (w

ww

.comp.dit.ie/bm

acnamee)

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2of55 Acknowledgments

These notes are based (heavily) on those provided by the authors to

accompany “Data Mining: Concepts & Techniques” by Jiawei Han and Micheline Kamber

Some slides are also based on trainer’s kits provided by

More information about the book is available at:www-sal.cs.uiuc.edu/~hanj/bk2/

And information on SAS is available at:www.sas.com

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3of55 Classification & PredictionToday we will look at:

– What are classification & prediction?– Issues regarding classification and prediction– Classification techniques:

• Case based reasoning (k-nearest neighbour algorithm)• Decision tree induction• Bayesian classification• Neural networks• Support vector machines (SVM)• Classification based on association rule mining concepts• Other classification methods

– Prediction– Classification accuracy

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4of55 Classification & PredictionClassification:

– 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

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Classification: A Two-Step Process

1) Model construction: – 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 is the training set

– A model created for classification

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Classification: A Two-Step Process (cont…)

2) Model usage:– Estimate accuracy of the model

• All members of an independent test-set is tested using the model built

• 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

– If the accuracy is acceptable, the model is used to classify data tuples whose class labels are not known

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Classification: Model Construction

IF rank = ‘professor’OR years > 6THEN tenured = ‘yes’

NAME RANK YEARS TENUREDMike Assistant Prof 3 noMary Assistant Prof 7 yesBill Professor 2 yesJim Associate Prof 7 yesDave Assistant Prof 6 noAnne Associate Prof 3 no

Training Set

Classification Model

Classification Algorithm

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Classification: Using The Model In Prediction

(Jeff, Professor, 4)

Tenured?

Testing Set

Classifier

Unseen Data

Yes

NAME RANK YEARS TENUREDTom Assistant Prof 2 noMerlisa Associate Prof 7 noGeorge Professor 5 yesJoseph Assistant Prof 7 yes

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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

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Issues Regarding Classification & Prediction: 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

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Issues Regarding Classification & Prediction: Evaluating Classification Methods

Predictive accuracySpeed 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 provided by the

model

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Classification Techniques: Case Based Reasoning (The k-Nearest Neighbor Algorithm)

Case based reasoning is a classification technique which uses prior examples (cases) to determine the classification of unknown cases

The k-nearest neighbour (k-NN) algorithm is the simplest form of case based reasoning

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The k-Nearest Neighbor Algorithm)

All instances correspond to points in n-D spaceThe nearest neighbours are defined in terms of Euclidean distance (or other appropriate measure)The target value can be discrete or real-valuedFor discrete targets, k-NN returns the most common value among the k training examples nearest to the queryFor real-valued targets, k-NN returns a combination (e.g. average) of the nearest neighbours’ target values

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14of55 Nearest Neighbour Example

Wave Size(ft)

Wave Period(secs)

6 15

1 6

5 11

7 10

6 11

2 1

3 4

6 12

4 2

GoodSurf?

Yes

No

Yes

Yes

Yes

No

No

Yes

No

Class

10 10 ?

Features

Query

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15of55 Nearest Neighbour Example

f1

f2

When a new case is to be classified:

– Calculate the distance from the new case to all training cases

– Put the new case in the same class as its nearest neighbour

?

?

?

Wave Period

Wave S

ize

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16of55 k-Nearest Neighbour Example

f1

f2

What about when it’s too close to call?

Use the k-nearest neighbour technique

– Determine the k nearest neighbours to the query case

– Put the new case into the same class as the majority of its nearest neighbours

Wave Period

Wave S

ize

?

2 neighbours

1 neighbourvs.

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Nearest Neighbour Distance Measures

Any kind of measurement can be used to calculate the distance between casesThe measurement most suitable will depend on the type of features in the problemEuclidean distance is the most used technique

where n is the number of features, ti is the ith feature of the training case and qi is the ith feature of the query case

n

iii qtd

1

2)(

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Summary Of Nearest Neighbour Classification

Strengths– No training involved – lazy learning– New data can be added on the fly– Some explanation capabilities– Robust to noisy data by averaging k-nearest

neighbors

Weaknesses– Not the most powerful classification– Slow classification– Curse of dimensionality

One of the easiest machine learning classification techniques to understand

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19of55 Case-Based ReasoningUses lazy evaluation and analysis of similar instancesHowever, instances are not necessarily “points in a Euclidean space”Methodology

– Instances represented by rich symbolic descriptions

– Multiple retrieved cases may be combined– Tight coupling between case retrieval,

knowledge-based reasoning, and problem solving

Lots of active research issues

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Classification Techniques: Decision Tree Induction

Decision trees are the most widely used classification technique in data mining today

Formulate problems into a tree composed of decision nodes (or branch nodes) and classification nodes (or leaf nodes)

Problem is solved by navigating down the tree until we reach an appropriate leaf node

The tricky bit is building the most efficient and powerful tree

J. Ross Quinlan is a famed researcher in

data mining and decision theory. He has done pioneering work in the area of

decision trees, including inventing the ID3 and C4.5

algorithms.

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21of55 Training Dataset

Age Income Student CreditRating BuysComputer

<=30 high no fair no

<=30 high no excellent no

31 - 40 high no fair yes

>40 medium no fair yes

>40 low yes fair yes

>40 low yes excellent no

31 - 40 low yes excellent yes

<=30 medium no fair no

<=30 low yes fair yes

>40 medium yes fair yes

<=30 medium yes excellent yes

31 - 40 medium no excellent yes

31 - 40 high yes fair yes

>40 medium no excellent no

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22of55 Resultant Decision Tree

Age?

Student?Credit

Rating?Yes

Yes YesNo No

<=30 30 - 40 >40

no yes excellent fair

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Algorithm For Decision Tree Induction

Basic algorithm (a greedy algorithm)– Tree is constructed in a top-down recursive

divide-and-conquer manner– At the 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)

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Algorithm For Decision Tree Induction

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

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The attribute selection mechanism used in ID3 and based on work on information theory by Claude Shannon

If our data is split into classes according to fractions {p1,p2…, pm} then the entropy is

measured as the info required to classify any arbitrary tuple as follows:

iim

pp,...,p,ppEm

i2

1

log)(21

Attribute Selection Measure: Information Gain (ID3/C4.5)

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The information measure is essentially the same as entropy

At the root node the information is as follows:

94.0

14

5log

14

5

14

9log

14

9

14

5

14

9]5,9[

22

,Einfo

Attribute Selection Measure: Information Gain (ID3/C4.5) (cont…)

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To measure the information at a particular attribute we measure info for the various splits of that attribute

Attribute Selection Measure: Information Gain (ID3/C4.5) (cont…)

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At the age attribute the information is as follows:

694.0

5

2log

5

2

5

3log

5

3

14

5

4

0log

4

0

4

4log

4

4

14

4

5

3log

5

3

5

2log

5

2

14

5

2,314

50,4

14

43,2

14

5]2,3[],0,4[],3,2[

22

22

22

infoinfoinfoinfo

Attribute Selection Measure: Information Gain (ID3/C4.5) (cont…)

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Attribute Selection Measure: Information Gain (ID3/C4.5) (cont…)

In order to determine which attributes we should use at each node we measure the information gained in moving from one node to another and choose the one that gives us the most information

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Attribute Selection By Information Gain Example

Class P: BuysComputer = “yes”

Class N: BuysComputer = “no”– I(p, n) = I(9, 5) =0.940

Compute the entropy for age:Age Income Student CreditRating BuysComputer

<=30 high no fair no

<=30 high no excellent no

31 - 40 high no fair yes

>40 medium no fair yes

>40 low yes fair yes

>40 low yes excellent no

31 - 40 low yes excellent yes

<=30 medium no fair no

<=30 low yes fair yes

>40 medium yes fair yes

<=30 medium yes excellent yes

31 - 40 medium no excellent yes

31 - 40 high yes fair yes

>40 medium no excellent no

Age pi ni I(pi, ni)

>=30 2 3 0.971

30 – 40 4 0 0

>40 3 2 0.971

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Attribute Selection By Information Gain Computation

means “age <=30” has 5 out of 14 samples,

with 2 yes and 3 no. Hence:

Similarly:

694.0

)2,3(14

5)0,4(

14

4)3,2(

14

5)(

IIIageE

048.0)_(

151.0)(

029.0)(

ratingcreditGain

studentGain

incomeGain

246.0)(),()( ageEnpIageGain

)3,2(14

5I

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Other Attribute Selection Measures

Gini index (CART, 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

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Extracting Classification Rules From Trees

Represent knowledge in the form of IF-THEN rules

One rule is created for each path from root to leaf

Each attribute-value pair along a path forms a conjunction

The leaf node holds the class prediction

Rules are easier for humans to understandIF Age = “<=30” AND Student = “no” THEN BuysComputer = “no”

IF Age = “<=30” AND Student = “yes” THEN BuysComputer = “yes”

IF Age = “31…40” THEN BuysComputer = “yes”

IF Age = “>40” AND CreditRating = “excellent” THEN BuysComputer = “yes”

IF Age = “<=30” AND CreditRating = “fair” THEN BuysComputer = “no”

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34of55 Overfitting

Training Set Test Set

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35of55 Overfitting (cont…)

Training Set Test Set

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Avoiding Overfitting In Classification

An induced tree may overfit the training data – Too many branches, some may reflect anomalies due to

noise or outliers– Poor accuracy for unseen samples

Two approaches to avoiding overfitting– Prepruning: Halt tree construction early

• Do not split a node if this would result in a measure of the usefullness of the tree falling below a threshold

• Difficult to choose an appropriate threshold

– Postpruning: Remove branches from a “fully grown” tree to give a sequence of progressively pruned trees

• Use a set of data different from the training data to decide which is the “best pruned tree”

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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 minimized

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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

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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

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Data Cube-Based Decision-Tree Induction

Integration of generalization with decision-tree induction

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

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Decision Tree In SAS

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42of55 Bayesian Classification: Why?Probabilistic learning:

– Calculate explicit probabilities for a hypothesis– Among the most practical approaches to certain types of

learning problemsIncremental:

– Each training example can incrementally increase/ decrease the probability that a hypothesis is correct

– Prior knowledge can be combined with observed dataProbabilistic prediction:

– Predict multiple hypotheses, weighted by their probabilities

Standard: – Bayesian methods can provide a standard of optimal

decision making against which other methods can be measured

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43of55 Bayesian Theorem: BasicsLet X be a data sample whose class label is unknown

Let H be a hypothesis that X belongs to class C

For classification problems, determine P(H|X): the probability that the hypothesis holds given the observed data sample X

– P(H): prior probability of hypothesis H (i.e. the initial probability before we observe any data, reflects the background knowledge)

– P(X): probability that sample data is observed

– P(X|H): probability of observing the sample X, given that the hypothesis holds

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44of55 Bayesian TheoremGiven training data X, posteriori probability of a hypothesis H, P(H|X) follows the Bayes theorem

Informally, this can be written as

MAP (maximum posteriori) hypothesis

Practical difficulty: require initial knowledge of many probabilities, significant computational cost

)()()|()|(

XPHPHXPXHP

.)()|(maxarg)|(maxarg hPhDPHh

DhPHhMAP

h

posterior = (likelihood * prior) / evidence

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45of55 Naïve Bayes Classifier A simplified assumption: attributes are conditionally independent:

The product of occurrence of say 2 elements x1 and x2, given the current class is C, is the product of the probabilities of each element taken separately, given the same class P([y1,y2],C) = P(y1,C) * P(y2,C)No dependence relation between attributes Greatly reduces the computation cost, only count the class distribution.

Once the probability P(X|Ci) is known, assign X to the class with maximum P(X|Ci)*P(Ci)

n

kCixkPCiXP

1)|()|(

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46of55 Training dataset

age income student credit_rating buys_computer<=30 high no fair no<=30 high no excellent no30…40 high no fair yes>40 medium no fair yes>40 low yes fair yes>40 low yes excellent no31…40 low yes excellent yes<=30 medium no fair no<=30 low yes fair yes>40 medium yes fair yes<=30 medium yes excellent yes31…40 medium no excellent yes31…40 high yes fair yes>40 medium no excellent no

Class:C1:buys_computer=‘yes’C2:buys_computer=‘no’

Data sample X =(age<=30,Income=medium,Student=yesCredit_rating=Fair)

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Naïve Bayesian Classifier: ExampleCompute P(X/Ci) for each class

P(age=“<30” | buys_computer=“yes”) = 2/9=0.222 P(age=“<30” | buys_computer=“no”) = 3/5 =0.6 P(income=“medium” | buys_computer=“yes”)= 4/9 =0.444 P(income=“medium” | buys_computer=“no”) = 2/5 = 0.4 P(student=“yes” | buys_computer=“yes)= 6/9 =0.667 P(student=“yes” | buys_computer=“no”)= 1/5=0.2 P(credit_rating=“fair” | buys_computer=“yes”)=6/9=0.667 P(credit_rating=“fair” | buys_computer=“no”)=2/5=0.4

X=(age<=30 ,income =medium, student=yes,credit_rating=fair)

P(X|Ci) : P(X|buys_computer=“yes”)= 0.222 x 0.444 x 0.667 x 0.0.667 =0.044 P(X|buys_computer=“no”)= 0.6 x 0.4 x 0.2 x 0.4 =0.019P(X|Ci)*P(Ci ) : P(X|buys_computer=“yes”) * P(buys_computer=“yes”)=0.028

P(X|buys_computer=“no”) * P(buys_computer=“no”)=0.007

X belongs to class “buys_computer=yes”

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Naïve Bayesian Classifier: Comments

Advantages : – Easy to implement – Good results obtained in most of the cases

Disadvantages– Assumption: class conditional independence , therefore

loss of accuracy– Practically, dependencies exist among variables – E.g., hospitals: patients: Profile: age, family history etc – Symptoms: fever, cough etc., Disease: lung cancer,

diabetes etc – Dependencies among these cannot be modeled by

Naïve Bayesian Classifier

How to deal with these dependencies?– Bayesian Belief Networks

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49of55 Bayesian NetworksBayesian belief network allows a subset of the variables conditionally independent

A graphical model of causal relationships– Represents dependency among the variables – Gives a specification of joint probability

distribution

X Y

ZP

•Nodes: random variables•Links: dependency•X,Y are the parents of Z, and Y is

the parent of P•No dependency between Z and P•Has no loops or cycles

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Bayesian Belief Network: An Example

FamilyHistory

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

Bayesian Belief Networks

The conditional probability table for the variable LungCancer:Shows the conditional probability for each possible combination of its parents

n

iZParents iziPznzP

1))(|(),...,1(

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51of55 Learning Bayesian NetworksSeveral cases

– Given both the network structure and all variables observable: learn only the CPTs

– Network structure known, some hidden variables: method of gradient descent, analogous to neural network learning

– Network structure unknown, all variables observable: search through the model space to reconstruct graph topology

– Unknown structure, all hidden variables: no good algorithms known for this purpose

D. Heckerman, Bayesian networks for data mining

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52of55 Lazy Vs. Eager LearningLazy learning:

– Case based reasoning

Eager learning:– Decision-tree and Bayesian classification

Key differences:– Lazy method may consider query instance when

deciding how to generalize beyond the training data D

– Eager method cannot since they have already chosen global approximation when seeing the query

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53of55 Lazy Vs. Eager LearningEfficiency:

– 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 learners must commit to a single hypothesis that covers the entire instance space

– Easier for lazy learners to cope with concept drift

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54of55 SummaryClassification is an extensively studied problem

Classification is probably one of the most widely used data mining techniques with a lot of extensions

Classification techniques can be categorized as either lazy or eager

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. classification of skewed data sets

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55of55 Questions?

?