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Decision Tree

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2 Outline l General Approach to Solving a Classification Problem l Decision Tree Induction

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3 Classification: Definition l Given a collection of records (training set ) –Each record contains a set of attributes, one of the attributes is the class. l Find a model for class attribute as a function of the values of other attributes. l 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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4 Illustrating Classification Task

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

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6 Classification Techniques l Decision Tree based Methods l Rule-based Methods l Memory based reasoning l Neural Networks l Naïve Bayes and Bayesian Belief Networks l Support Vector Machines

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7 Outline l General Approach to Solving a Classification Problem l Decision Tree Induction l Model Overfitting l Evaluating the Performance of a Classifier l Methods for Comparing Classifiers

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8 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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9 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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10 Decision Tree Classification Task Decision Tree

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11 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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12 Apply Model to Test Data Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Test Data

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

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

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

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16 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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17 Decision Tree Classification Task Decision Tree

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

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19 General Structure of Hunt’s Algorithm l Let D t be the set of training records that reach a node t l General Procedure: –If D t contains records that 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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20 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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21 Tree Induction l Greedy strategy. –Split the records based on an attribute test that optimizes certain criterion. l 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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22 Tree Induction l Greedy strategy. –Split the records based on an attribute test that optimizes certain criterion. l 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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23 How to Specify Test Condition? l Depends on attribute types –Nominal –Ordinal –Continuous l Depends on number of ways to split –2-way split –Multi-way split

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24 Splitting Based on Nominal Attributes l Multi-way split: Use as many partitions as distinct values. l 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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25 l Multi-way split: Use as many partitions as distinct values. l Binary split: Divides values into two subsets. Need to find optimal partitioning. l 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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26 Splitting Based on Continuous Attributes l 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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27 Splitting Based on Continuous Attributes

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28 Tree Induction l Greedy strategy. –Split the records based on an attribute test that optimizes certain criterion. l 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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29 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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30 How to determine the Best Split l Greedy approach: –Nodes with homogeneous class distribution are preferred l Need a measure of node impurity: Non-homogeneous, High degree of impurity Homogeneous, Low degree of impurity

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31 Measures of Node Impurity l Gini Index l Entropy l Misclassification error

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32 How to Find the Best Split B? YesNo Node N3Node N4 A? YesNo Node N1Node N2 Before Splitting: M0 M1 M2M3M4 M12 M34 Gain = M0 – M12 vs M0 – M34

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33 Measure of Impurity: GINI l Gini Index for a given node t : (NOTE: p( j | t) is the relative frequency of class j at node t). –Maximum (1 - 1/n c ) 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

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34 Examples for computing GINI P(C1) = 0/6 = 0 P(C2) = 6/6 = 1 Gini = 1 – P(C1) 2 – P(C2) 2 = 1 – 0 – 1 = 0 P(C1) = 1/6 P(C2) = 5/6 Gini = 1 – (1/6) 2 – (5/6) 2 = P(C1) = 2/6 P(C2) = 4/6 Gini = 1 – (2/6) 2 – (4/6) 2 = 0.444

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35 Splitting Based on GINI l Used in CART, SLIQ, SPRINT. l When a node p is split into k partitions (children), the quality of split is computed as, where,n i = number of records at child i, n = number of records at node p.

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36 Binary Attributes: Computing GINI Index l Splits into two partitions l Effect of Weighing partitions: –Larger and Purer Partitions are sought for. B? YesNo Node N1Node N2 Gini(N1) = 1 – (5/7) 2 – (2/7) 2 = Gini(N2) = 1 – (1/5) 2 – (4/5) 2 = 0.32 Gini(Children) = 7/12 * /12 * 0.32 = 0.371

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37 Categorical Attributes: Computing Gini Index l For each distinct value, gather counts for each class in the dataset l Use the count matrix to make decisions Multi-way splitTwo-way split (find best partition of values)

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38 Alternative Splitting Criteria based on INFO l 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 n c ) when records are equally distributed among all classes implying least information Minimum (0.0) when all records belong to one class, implying most information –Entropy based computations are similar to the GINI index computations

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39 Examples for computing Entropy P(C1) = 0/6 = 0 P(C2) = 6/6 = 1 Entropy = – 0 log 0 – 1 log 1 = – 0 – 0 = 0 P(C1) = 1/6 P(C2) = 5/6 Entropy = – (1/6) log 2 (1/6) – (5/6) log 2 (1/6) = 0.65 P(C1) = 2/6 P(C2) = 4/6 Entropy = – (2/6) log 2 (2/6) – (4/6) log 2 (4/6) = 0.92

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40 Splitting Based on INFO... l Information Gain: Parent Node, p is split into k partitions; n i is 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.

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41 Splitting Based on INFO... l Gain Ratio: Parent Node, p is split into k partitions n i is the number of records in partition i –Adjusts Information Gain by the entropy of the partitioning (SplitINFO). Higher entropy partitioning (large number of small partitions) is penalized! –Used in C4.5 –Designed to overcome the disadvantage of Information Gain

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42 Splitting Criteria based on Classification Error l Classification error at a node t : l Measures misclassification error made by a node. Maximum (1 - 1/n c ) 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

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43 Examples for Computing Error P(C1) = 0/6 = 0 P(C2) = 6/6 = 1 Error = 1 – max (0, 1) = 1 – 1 = 0 P(C1) = 1/6 P(C2) = 5/6 Error = 1 – max (1/6, 5/6) = 1 – 5/6 = 1/6 P(C1) = 2/6 P(C2) = 4/6 Error = 1 – max (2/6, 4/6) = 1 – 4/6 = 1/3

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44 Comparison among Splitting Criteria For a 2-class problem:

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45 Misclassification Error vs Gini A? YesNo Node N1Node N2 Gini(N1) = 1 – (3/3) 2 – (0/3) 2 = 0 Gini(N2) = 1 – (4/7) 2 – (3/7) 2 = Gini(Children) = 3/10 * 0 + 7/10 * = Gini improves !!

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46 Tree Induction l Greedy strategy. –Split the records based on an attribute test that optimizes certain criterion. l 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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47 Stopping Criteria for Tree Induction l Stop expanding a node when all the records belong to the same class l Stop expanding a node when all the records have similar attribute values l Early termination (to be discussed later)

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48 Decision Tree Based Classification l Advantages: –Inexpensive to construct –Extremely fast at classifying unknown records –Easy to interpret for small-sized trees –Accuracy is comparable to other classification techniques for many simple data sets

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49 Example: C4.5 l Simple depth-first construction. l Uses Information Gain Ratio l Sorts Continuous Attributes at each node. l Needs entire data to fit in memory. l Unsuitable for Large Datasets. –Needs out-of-core sorting. l You can download the software from:

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