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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 the values of other attributes. Goal: previously unseen records should be assigned a class as accurately as possible. –A test set is 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

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Examples of Classification Task Predicting tumor cells as benign or malignant Classifying credit card transactions as legitimate or fraudulent Classifying secondary structures of protein as alpha-helix, beta-sheet, or random coil Categorizing news stories as finance, weather, entertainment, sports, etc

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Classification Techniques Decision Tree based Methods Rule-based Methods Neural Networks Naïve Bayes and Bayesian Belief Networks Support Vector Machines Logistic Regression

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Example of a Decision Tree categorical continuous class Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Splitting Attributes Training Data Model: Decision Tree

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Another Example of Decision Tree categorical continuous class MarSt Refund TaxInc YES NO Yes No Married Single, Divorced < 80K> 80K There could be more than one tree that fits the same data!

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Decision Tree Classification Task Decision Tree

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Apply Model to Test Data Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Test Data Start from the root of tree.

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Apply Model to Test Data Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Test Data

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Apply Model to Test Data Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Test Data

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Apply Model to Test Data Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Test Data

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Apply Model to Test Data Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Test Data

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Apply Model to Test Data Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Test Data Assign Cheat to “No”

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Decision Tree Classification Task Decision Tree

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Decision Tree Induction Many Algorithms: –Hunt’s Algorithm (one of the earliest) –CART –ID3, C4.5 –SLIQ,SPRINT

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General Structure of Hunt’s Algorithm Let D t be the set of training records that reach a node t General Procedure: –If D t contains records that all belong the same class y t, then t is a leaf node labeled as y t –If D t is an empty set, then t is a leaf node labeled by the default class, y d –If D t contains records that belong to more than one class, use an attribute test to split the data into smaller subsets. Recursively apply the procedure to each subset. DtDt ?

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Hunt’s Algorithm Don’t Cheat Refund Don’t Cheat Don’t Cheat YesNo Refund Don’t Cheat YesNo Marital Status Don’t Cheat Single, Divorced Married Taxable Income Don’t Cheat < 80K>= 80K Refund Don’t Cheat YesNo Marital Status Don’t Cheat Single, Divorced Married

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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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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 as distinct values. Binary split: Divides values into two subsets. Need to find optimal partitioning. CarType Family 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 Size Small Medium Large Size {Medium, Large} {Small} Size {Small, Medium} {Large} OR Size {Small, Large} {Medium}

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Splitting Based on Continuous Attributes Different ways of handling –Discretization to form an ordinal categorical attribute Static – discretize once at the beginning Dynamic – ranges can be found by equal interval bucketing, 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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Splitting Based on Continuous Attributes

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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 determine the Best Split 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 Greedy approach: –Nodes with homogeneous class distribution are preferred Need a measure of node impurity: 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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1 Data Mining Lecture 3: Decision Trees. 2 Classification: Definition l Given a collection of records (training set ) –Each record contains a set of attributes,

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