Data Mining: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– Training data are analyzed by a classification algorithm

– The class label attribute is credit_rating

– 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

• After the analysis, can you classify the following patterns?– (Black, Gold, Tall)– (Blue, White, Short)

• Example distributions

BlackShort

BlackTall

WhiteShort

WhiteTall

GoldShort

GoldTall

Black + + + + ?

Brown + + ─

Blue ─ ? ─ ─ ─

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

Another Example

Another Example

Decision Tree Generation Algorithm: ID3

Decision Tree Generation Algorithm: ID3

Decision Tree Generation Algorithm: ID3

Gini Index• If a data set T contains examples from n classes, gi

ni 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

n

jj

p)T(gini1

21

)(giniN

)(giniN

)T( TNTNginisplit 2

21

1

Inference Power of an Attribute

• 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”

Generating Classification Rules