data mining techniques: classification

Data Mining Techniques:Classification

Classification

• What is Classification?– Classifying tuples in a database

– In training set E• each tuple consists of the same set of multiple attributes

as the tuples in the large database W

• additionally, each tuple has a known class identity

– Derive the classification mechanism from the training set E, and then use this mechanism to classify general data (in W)

Learning Phase

• Learning– The class label attribute is credit_rating– Training data are analyzed by a classification algorithm– The classifier is represented in the form of classification rules

Testing Phase

• Testing (Classification)– Test data are used to estimate the accuracy of the classification rules

– If the accuracy is considered acceptable, the rules can be applied to the classification of new data tuples

Classification by Decision Tree

A top-down decision tree generation algorithm: ID-3 and its extended version C4.5 (Quinlan’93): J.R. Quinlan, C4.5 Programs for Machine Learning, Morgan Kaufmann, 1993

Decision Tree Generation• At start, all the training examples are at the root

• Partition examples recursively based on selected attributes

• Attribute Selection– Favoring the partitioning which makes the majority

of examples belong to a single class

• Tree Pruning (Overfitting Problem)– Aiming at removing tree branches that may lead to

errors when classifying test data• Training data may contain noise, …

Eye Hair Height OrientalBlack Black Short YesBlack White Tall YesBlack White Short YesBlack Black Tall YesBrown Black Tall YesBrown White Short YesBlue Gold Tall NoBlue Gold Short NoBlue White Tall NoBlue Black Short No

Brown Gold Short No

1 2 3 4 5 6 7 8 91011

Another Examples

Decision Tree

Decision Tree

Decision Tree Generation

• Attribute Selection (Split Criterion)– Information Gain (ID3/C4.5/See5)– Gini Index (CART/IBM Intelligent Miner)– Inference Power

• These measures are also called goodness functions and used to select the attribute to split at a tree node during the tree generation phase

Decision Tree Generation

• Branching Scheme– Determining the tree branch to which a sample

belongs– Binary vs. K-ary Splitting

• When to stop the further splitting of a node– Impurity Measure

• Labeling Rule– A node is labeled as the class to which most sa

mples at the node belongs

Decision Tree Generation Algorithm: ID3

(7.1) Entropy

ID: Iterative Dichotomiser

Decision Tree Algorithm: ID3

Decision Tree Algorithm: ID3

Decision Tree Algorithm: ID3

Decision Tree Algorithm: ID3

yes

Decision Tree Algorithm: ID3

Exercise 2

Decision Tree Generation Algorithm: ID3

Decision Tree Generation Algorithm: ID3

Decision Tree Generation Algorithm: ID3

How to Use a Tree• Directly

– Test the attribute value of unknown sample against the tree.

– A path is traced from root to a leaf which holds the label

• Indirectly– Decision tree is converted to classification rules– One rule is created for each path from the root

to a leaf– IF-THEN is easier for humans to understand

Generating Classification Rules

Generating Classification Rules

Generating Classification Rules• There are 4 decision rules are generated by the tree

– Watch the game and home team wins and out with friends then bear

– Watch the game and home team wins and sitting at home then diet soda

– Watch the game and home team loses and out with friend then bear

– Watch the game and home team loses and sitting at home then milk

• Optimization for these rules– Watch the game and out with friends then bear– Watch the game and home team wins and sitting at home then diet

soda– Watch the game and home team loses and sitting at home then

milk

Decision Tree Generation Algorithm: ID3

• All attributes are assumed to be categorical (discretized)

• Can be modified for continuous-valued attributes– Dynamically define new discrete-valued attributes that

partition the continuous attribute value into a discrete set of intervals

– A V | A < V

• Prefer Attributes with Many Values• Cannot Handle Missing Attribute Values• Attribute dependencies do not consider in this al

gorithm

Attribute Selection in C4.5

Handling Continuous Attributes

Handling Continuous Attributes

Handling Continuous Attributes

Sorted By Sorted By

First Cut

Second

Cut

Third

Cut

Handling Continuous Attributes

Root

Price On Date T+1> 18.02

Price On Date T+1<= 18.02

Price On Date T> 17.84

Price On Date T<= 17.84

Price On Date T+1> 17.70

Price On Date T+1<= 17.70

Buy

Sell

Buy Sell

First Cut

Second Cut

Third Cut

Exercise 3:分析房價

SF : Square Feet

ID Location Type Miles SF CM Home Price (K)

1 Urban Detached 2 2000 50 High

2 Rural Detached 9 2000 5 Low

3 Urban Attached 3 1500 150 High

4 Urban Detached 15 2500 250 High

5 Rural Detached 30 3000 1 Low

6 Rural Detached 3 2500 10 Medium

7 Rural Detached 20 1800 5 Medium

8 Urban Attached 5 1800 50 High

9 Rural Detached 30 3000 1 Low

10 Urban Attached 25 1200 100 Medium

CM : No. of Homes in Community

Unknown Attribute Values in C4.5

Training

Testing

Unknown Attribute Values Adjustment of Attribute

Selection Measure

Fill in Approach

Probability Approach

Probability Approach

Unknown Attribute Values Partitioning the

Training Set

Probability Approach

Unknown Attribute Values Classifying an

Unseen Case

Probability Approach

Evaluation – Coincidence MatrixCost = $190 * (closing good account) + $10 * (keeping bad account open)

Accuracy (正確率 ) = (36+632) / 718 = 93.0%

Precision (精確率 ) for Insolvent = 36/58 = 62.01%Recall (捕捉率 ) for Insolvent = 36/64 = 56.25%F Measure = 2 * Precision * Recall / (Precision + Recall ) = 2 * 62.01% * 56.25% / (62.01% + 56.25% ) = 0.7 / 1.1826 = 0.59

Cost = $190 * 22 + $10 * 28 = $4,460

Decision Tree Model

Decision Tree Generation Algorithm: Gini Index

• If a data set S contains examples from n classes, gini index, gini(S), is defined as

where pj is the relative frequency of class Cj in S.

• If a data set S is split into two subsets S1 and S2 with sizes N1 and N2 respectively, the gini index of the split data contains examples from n classes, the gini index, gini(S), is defined as

n

1j

2jp1gini(S)

)Tgini(NN)Tgini(

NN(S)gini 2

21

1split

Decision Tree Generation Algorithm: Gini Index

• The attribute provides the smallest ginisplit(S) is chosen to split the node

• The computation cost of gini index is less than information gain

• All attributes are binary splitting in IBM Intelligent Miner– A V | A < V

Decision Tree Generation Algorithm: Inference Power

• A feature that is useful in inferring the group identity of a data tuple is said to have a good inference power to that group identity.

• In Table 1, given attributes (features) “Gender”, “Beverage”, “State”, try to find their inference power to “Group id”

Naive Bayesian Classification

• Each data sample is a n-dim feature vector– X = (x1, x2, .. xn) for attributes A1, A2, … An

• Suppose there are m classes– C = {C1, C2,.. Cm}

• The classifier will predict X to the class Ci that has the highest posterior probability, conditioned on X– X belongs to Ci iff P(Ci|X) > P(Cj|X) for all 1<

=j<=m, j!=i

Naive Bayesian Classification

• P(Ci|X) = P(X|Ci) P(Ci) / P(X)– P(Ci|X) = P(Ci X) / P(X) ; P(X|Ci) = P(Ci X) / P(Ci)∪ ∪

=> P(Ci|X) P(X) = P(X|Ci) P(Ci)

• P(Ci) = si / s– si is the number of training sample of class Ci – s is the total number of training samples

• Assumption: Independent between Attributes– P(X|Ci) = P(x1|Ci) P(x2|Ci) P(x3|Ci) ...

P(xn|Ci)

• P(X) can be ignored

Naive Bayesian Classification

Classify X=(age=“<=30”, income=“medium”, student=“yes”, credit-rating=“fair”)– P(buys_computer=yes) = 9/14

– P(buys_computer=no)=5/14

– P(age=<30|buys_computer=yes)=2/9

– P(age=<30|buys_computer=no)=3/5

– P(income=medium|buys_computer=yes)=4/9

– P(income=medium|buys_computer=no)=2/5

– P(student=yes|buys_computer=yes)=6/9

– P(student=yes|buys_computer=no)=1/5

– P(credit-rating=fair|buys_computer=yes)=6/9

– P(credit-rating =fair|buys_computer=no)=2/5

– P(X|buys_computer=yes)=0.044

– P(X|buys_computer=no)=0.019

– P(buys_computer=yes|X) = P(X|buys_computer=yes) P(buys_computer=yes)=0.028

– P(buys_computer=no|X) = P(X|buys_computer=no) P(buys_computer=no)=0.007

Homework Assignment