Bab 07 - Class & Predict - Part 1.ppt

8/12/2019 Bab 07 - Class & Predict - Part 1.ppt

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Data Mining Arif Djunaidy FTIF ITS Bab 7-1 - 1/52

Data Mining

Bab 7 Part 1

Classification & Prediction


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Classification: predicts categorical class labels

classifies data (constructs a model) based on the training set andthe values (class labels)in a classifying attribute and uses it inclassifying 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


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Classification: Definition

Given a collection of records (training set ) Each record contains a set of attributes, one of the attributes is the

class.

Find a model for class attribute as a function of thevalues of other attributes.

Goal:previously unseenrecords should be assigned aclass as accurately as possible. A test setis used to determine the accuracy of the model. Usually, the

given data set is divided into training and test sets, with training set

used to build the model and test set used to validate it.


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Illustrating Classification Task

Apply

Model

Induction

Deduction

Learn

Model

Model

Tid Attrib1

Attrib2 Attrib3 Class

1

Yes Large 125K

No

2

No Medium 100K

No

3

No Small 70K

No

4

Yes Medium 120K

No

5

No Large 95K

Yes

6

No Medium 60K

No

7

Yes Large 220K

No

8

No Small 85K

Yes

9

No Medium 75K

No

10

No Small 90K

Yes10

Tid Attrib1

Attrib2 Attrib3 Class

11

No Small 55K

?

12

Yes Medium 80K

?

13

Yes Large 110K

?

14

No Small 95K

?

15

No Large 67K

?10

Test Set

Learning

algorithm

Training Set


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Examples of Classification Task

Predicting tumor cells as benign or malignant

Classifying credit card transactionsas legitimate or fraudulent

Classifying secondary structures of proteinas alpha-helix, beta-sheet, or randomcoil

Categorizing news stories as finance,weather, entertainment, sports, etc


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ClassificationA Two-Step Process

Model construction (induction): 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, ormathematical formulae

Model usage (deduction): for classifying future or unknown objects Estimate accuracy of the model

The known label of test sample is compared with the classified resultfrom 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-fittingwill occur


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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 and prediction:(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 regarding classification and prediction:

(2) Evaluating Classification Methods

Predictive accuracy Speed

time to construct the model time to use the model

Robustness handling noise and missing values

Scalability efficiency in disk-resident databases



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



Example of a Decision Tree

Tid Refund MaritalStatus

TaxableIncome Cheat

1 Yes Single 125K No

2 No Married 100K No

3 No Single 70K No

4 Yes Married 120K No

5 No Divorced 95K Yes

6 No Married 60K No

7 Yes Divorced 220K No

8 No Single 85K Yes

9 No Married 75K No

10 No Single 90K Yes10

Refund

MarSt

TaxInc

YESNO

NO

NO

Yes No

MarriedSingle, Divorced

< 80K > 80K

Spl i t t ing Attr ibutes

Training Data Model: Decision Tree



Another Example of Decision Tree


TaxableIncome Cheat



3 No Single 70K No



6 No Married 60K No


8 No Single 85K Yes

9 No Married 75K No


MarSt

Refund

TaxInc

YESNO

NO

NO

Yes No

MarriedSingle,

Divorced

< 80K > 80K

There could be more than one tree thatfits the same data !


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Decision Tree Classification Task

Apply

Model

Induction

Deduction

Learn

Model

Model

Tid Attrib1 Attrib2 Attrib3 Class

1 Yes Large 125K No

2 No Medium 100K No

3 No Small 70K No

4 Yes Medium 120K No

5 No Large 95K Yes

6 No Medium 60K No

7 Yes Large 220K No

8 No Small 85K Yes

9 No Medium 75K No

10 No Small 90K Yes10


11 No Small 55K ?

12 Yes Medium 80K ?

13 Yes Large 110K ?

14 No Small 95K ?

15 No Large 67K ?10

Test Set

TreeInduction

algorithm

Training Set

Decision

Tree


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Apply Model to Test Data (1)

Refund

MarSt

TaxInc

YESNO

NO

NO

Yes No


< 80K > 80K

Refund MaritalStatus

TaxableIncome Cheat

No Married 80K ?10

Test Data

Start from the root of tree.


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Refund

MarSt

TaxInc

YESNO

NO

NO

Yes No


< 80K > 80K


TaxableIncome Cheat

No Married 80K ?10

Test Data



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Refund

MarSt

TaxInc

YESNO

NO

NO

Yes No


< 80K > 80K


TaxableIncome Cheat

No Married 80K ?10

Test Data



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Refund

MarSt

TaxInc

YESNO

NO

NO

Yes No


< 80K > 80K


TaxableIncome Cheat

No Married 80K ?10

Test Data



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Refund

MarSt

TaxInc

YESNO

NO

NO

Yes No


< 80K > 80K


TaxableIncome Cheat

No Married 80K ?10

Test Data



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Refund

MarSt

TaxInc

YESNO

NO

NO

Yes No


< 80K > 80K


TaxableIncome Cheat

No Married 80K ?10

Test Data

Assign Cheat to No



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Decision Tree Classification Task

Apply

Model

Induction

Deduction

Learn

Model

Model


1 Yes Large 125K No

2 No Medium 100K No

3 No Small 70K No

4 Yes Medium 120K No

5 No Large 95K Yes

6 No Medium 60K No

7 Yes Large 220K No

8 No Small 85K Yes

9 No Medium 75K No

10 No Small 90K Yes10


11 No Small 55K ?

12 Yes Medium 80K ?

13 Yes Large 110K ?

14 No Small 95K ?

15 No Large 67K ?10

Test Set

TreeInduction

algorithm

Training Set

Decision Tree


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Algorithm for Decision Tree Induction

Basic algorithm Tree is constructed in a top-down recursive manner

At start, all the training examples are at the root

Attributes are categorical (if continuous-valued, they are discretized inadvance)

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 majorityvotingis employed for classifying the leaf

There are no samples left


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Decision Tree Induction

Many Algorithms exist, for examples:

Hunts Algorithm (one of the earliest)

CART

ID3, C4.5

SLIQ, SPRINT


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General Structure of HuntsAlgorithm

Let Dtbe the set of trainingrecords that reach a node t

General Procedure: If D

t

contains records that belongthe same class yt, then t is a leafnode labeled as yt

If Dtis an empty set, then t is aleaf node labeled by the defaultclass, yd

If Dtcontains records that belongto more than one class, use anattribute test to split the data intosmaller subsets. Recursivelyapply the procedure to eachsubset.


TaxableIncome Cheat



3 No Single 70K No



6 No Married 60K No


8 No Single 85K Yes

9 No Married 75K No


Dt

?


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Hunts Algorithm

Dont

Cheat

Refund

Dont

Cheat

Dont

Cheat

Yes No

Refund

Dont

Cheat

Yes No

Marital

Status

Dont

Cheat

Cheat

Single,

DivorcedMarried

Taxable

Income

Dont

Cheat

< 80K >= 80K

Refund

Dont

Cheat

Yes No

Marital

Status

Dont

CheatCheat

Single,

DivorcedMarried


TaxableIncome Cheat



3 No Single 70K No



6 No Married 60K No


8 No Single 85K Yes

9 No Married 75K No



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Tree Induction

Greedy strategy.

Split the records based on an attribute test that

optimizes certain criterion.

Issues

Determine how to split the records

How to specify the attribute test condition?

How to determine the best split?

Determine when to stop splitting


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How to Specify Test Condition?

Depends on attribute types

Nominal

Ordinal

Continuous

Depends on number of ways to split

2-way split

Multi-way split


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Splitting Based on Nominal Attributes

Multi-way split:Use as many partitions asdistinct values.

Binary split: Divides values into two subsets.Need to find optimal partitioning.

CarTypeFamily

Sports

Luxury

CarType{Family,

Luxury} {Sports}

CarType{Sports,

Luxury} {Family}OR


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Multi-way split:Use as many partitions as

distinct values.

Binary split: Divides values into two subsets.Need to find optimal partitioning.

What about this split?

Splitting Based on Ordinal Attributes

SizeSmall

Medium

Large

Size{Medium,

Large} {Small}

Size{Small,

Medium} {Large}

OR

Size{Small,

Large} {Medium}


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Splitting Based on Continuous Attributes (1)

Different ways of handling Discretizationto form an ordinal categorical attribute

Staticdiscretize once at the beginning

Dynamicranges can be found by equal intervalbucketing, equal frequency bucketing

(percentiles), or clustering.

Binary Decision: (A < v) or (A v) consider all possible splits and finds the best cut

can be more compute intensive


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Taxable

Income

> 80K?

Yes No

Taxable

Income?

(i) Binary split (ii) Multi-way split

< 10K

[10K,25K) [25K,50K) [50K,80K)

> 80K

Splitting Based on Continuous Attributes (2)


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Tree Induction

Greedy strategy.

Split the records based on an attribute test thatoptimizes certain criterion.

Issues

Determine how to split the records

How to specify the attribute test condition?

How to determine the best split?

Determine when to stop splitting


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How to determine the Best Split (1)

Own

Car?

C0: 6

C1: 4

C0: 4

C1: 6

C0: 1

C1: 3

C0: 8

C1: 0

C0: 1

C1: 7

Car

Type?

C0: 1

C1: 0

C0: 1

C1: 0

C0: 0

C1: 1

Student

ID?

...

Yes NoFamily

Sports

Luxury c1 c

10

c20

C0: 0

C1: 1...

c11

Before Splitting: 10 records of class 0,

10 records of class 1

Which test condition is the best?


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How to determine the Best Split (2)

Greedy approach:

Nodes with homogeneousclass distribution arepreferred

Need a measure of node impurity:

C0: 5

C1: 5

C0: 9

C1: 1

Non-homogeneous,

High degree of impurity

Homogeneous,

Low degree of impurity


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Measures of Node Impurity

Gini Index

Entropy

Misclassification error


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How to Find the Best Split

B?

Yes No

Node N3 Node N4

A?

Yes No

Node N1 Node N2

Before Splitting:

C0 N10

C1 N11

C0 N20

C1 N21

C0 N30

C1 N31

C0 N40

C1 N41

C0 N00

C1 N01M0

M1 M2 M3 M4

M12 M34Gain= M0M12 vs. M0M34


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Measure of Impurity: GINI

Gini Index for a given node t :

(NOTE:p( j | t) is the relative frequency of class j at node t).

Maximum (1 - 1/nc) when records are equally distributed amongall classes, implying least interesting information

Minimum (0.0) when all records belong to one class, implyingmost interesting information

j

tjptGINI 2)]|([1)(

C1 0

C2 6

Gini=0.000

C1 2

C2 4

Gini=0.444

C1 3

C2 3

Gini=0.500

C1 1

C2 5

Gini=0.278


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Examples for computing GINI

C1 0

C2 6

C1 2

C2 4

C1 1

C2 5

P(C1) = 0/6 = 0 P(C2) = 6/6 = 1

Gini = 1P(C1)2P(C2)2= 101 = 0

j

tjptGINI 2)]|([1)(

P(C1) = 1/6 P(C2) = 5/6

Gini = 1(1/6)2(5/6)2= 0.278

P(C1) = 2/6 P(C2) = 4/6

Gini = 1(2/6)2(4/6)2= 0.444


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Splitting Based on GINI Used in CART, SLIQ, SPRINT.

When a node p is split into k partitions (children), thequality of split is computed as,

where, ni= number of records at child i,

n = number of records at node p.

k

i

i

split iGINIn

n

GINI 1 )(

Binary Attributes:


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Binary Attributes:Computing GINI Index

Splits into two partitions Effect of Weighing partitions:

Larger and Purer Partitions are sought for.

B?

Yes No

Node N1 Node N2

Parent

C1 6

C2 6

Gini = 0.500

N1 N2C1 5 1

C2 2 4

Gini=0.371

Gini(N1)

= 1(5/7)2(2/7)2

= 0.408

Gini(N2)

= 1(1/5)2(4/5)2

= 0.32

Gini(Children)= 7/12 * 0.408 +

5/12 * 0.32

= 0.371

Categorical Attributes:


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Categorical Attributes:Computing Gini Index

For each distinct value, gather counts for each class inthe dataset

Use the count matrix to make decisions

CarType

{Sports,Luxury}

{Family}

C1 3 1

C2 2 4Gini 0.400

CarType

{Sports}{Family,Luxury}

C1 2 2

C2 1 5Gini 0.419

CarType

Family Sports Luxury

C1 1 2 1

C2 4 1 1Gini 0.393

Multi-way split Two-way split

(find best partition of values)

C ti Att ib t


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Continuous Attributes:Computing Gini Index

Use Binary Decisions based on onevalue

Several Choices for the splitting value Number of possible splitting values

= Number of distinct values

Each splitting value has a count matrixassociated with it Class counts in each of the partitions, A

< v and A v

Simple method to choose best v For each v, scan the database to gather

count matrix and compute its Gini index Computationally Inefficient! Repetition

of work.


TaxableIncome Cheat



3 No Single 70K No



6 No Married 60K No


8 No Single 85K Yes

9 No Married 75K No


TaxableIncome

> 80K?

Yes No

Continuous Attributes:


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Continuous Attributes:Computing Gini Index... For efficient computation: for each attribute,

Sort the attribute on values Linearly scan these values, each time updating the count matrix and

computing gini index

Choose the split position that has the least gini index

Cheat No No No Yes Yes Yes No No No No

Taxable Income

60 70 75 85 90 95 100 120 125 220

55 65 72 80 87 92 97 110 122 172 230

Yes 0 3 0 3 0 3 0 3 1 2 2 1 3 0 3 0 3 0 3 0 3 0

No 0 7 1 6 2 5 3 4 3 4 3 4 3 4 4 3 5 2 6 1 7 0

Gini 0.420 0.400 0.375 0.343 0.417 0.400 0.300 0.343 0.375 0.400 0.420

Split Positions

Sorted Values

Alt tiv S litti C it i


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Alternative Splitting Criteriabased on INFO

Entropy at a given node t:

(NOTE:p( j | t) is the relative frequency of class j at node t).

Measures homogeneity of a node. Maximum (log nc) when records are equally distributed among all

classes implying least information

Minimum (0.0) when all records belong to one class, implyingmost information

Entropy based computations are similar to the GINIindex computations

j

tjptjptEntropy )|(log)|()(


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Examples for computing Entropy

C1 0

C2 6

C1 2

C2 4

C1 1

C2 5

P(C1) = 0/6 = 0 P(C2) = 6/6 = 1

Entropy =0 log 01 log 1 =00 = 0

P(C1) = 1/6 P(C2) = 5/6

Entropy =(1/6) log2(1/6)(5/6) log2(1/6) = 0.65

P(C1) = 2/6 P(C2) = 4/6

Entropy =(2/6) log2(2/6)(4/6) log2(4/6) = 0.92

j

tjptjptEntropy )|(log)|()(2


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Splitting Based on INFO...

Information Gain:

Parent Node, p is split into k partitions;

niis number of records in partition i

Measures Reduction in Entropy achieved because of the split.Choose the split that achieves most reduction (maximizes GAIN)

Used in ID3 and C4.5

Disadvantage:Tends to prefer splits that result in large number of

partitions, each being small but pure.

k

i

i

spl itiEntropy

n

npEntropyGAIN

1

)()(


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age income student credit_rating40 low yes fair>40 low yes excellent3140 low yes excellent


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Attribute Selection byInformation 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)

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

studentGainincomeGain

25.069.094.0)(),()( ageEnpIageGain


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Splitting Based on INFO: Gain Ratio

Gain Ratio:

Parent Node, p is split into k partitions

niis the number of records in partition i

Adjusts Information Gain by the entropy of the partitioning(SplitINFO). Higher entropy partitioning (large number of smallpartitions) is penalized!

Used in C4.5

Designed to overcome the disadvantage of Information Gain

SplitINFO

GAINGainRATIO Split

spli t

k

i

ii

n

n

n

nSplitINFO

1log

Splitting Criteria based on


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Splitting Criteria based onClassification Error

Classification error at a node t :

Measures misclassification error made by a node. Maximum (1 - 1/nc) when records are equally distributed

among all classes, implying least interesting information Minimum (0.0) when all records belong to one class, implying

most interesting information

)|(max1)( tiPtError i


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Examples for Computing Error

C1 0

C2 6

C1 2

C2 4

C1 1

C2 5

P(C1) = 0/6 = 0 P(C2) = 6/6 = 1

Error = 1max (0, 1) = 11 = 0

P(C1) = 1/6 P(C2) = 5/6

Error = 1max (1/6, 5/6) = 15/6 = 1/6

P(C1) = 2/6 P(C2) = 4/6

Error = 1max (2/6, 4/6) = 14/6 = 1/3

)|(max1)( tiPtErrori


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Akhir

Bab 7 Part 1

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Bab 07 - Class & Predict - Part 1.ppt