1. Data Mining Classification: Basic Concepts, Decision Trees, and Model Evaluation COSC 4368

2. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Classification: Definition o Given a collection of records (training set ) –Each record contains a set of attributes, one of the attributes is the class. o Find a model for the class attribute as a function of the values of other attributes. o 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.

3. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Illustrating Classification Task

4. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Examples of Classification Task o Predicting tumor cells as benign or malignant o Classifying credit card transactions as legitimate or fraudulent o Classifying secondary structures of protein as alpha-helix, beta-sheet, or random coil o Categorizing news stories as finance, weather, entertainment, sports, etc

5. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Classification Techniques o Decision Tree based Methods o Rule-based Methods o Memory based reasoning, instance-based learning o Neural Networks o Naïve Bayes and Bayesian Belief Networks o Support Vector Machines

6. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 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

7. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 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!

8. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Decision Tree Classification Task Decision Tree

9. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Apply Model to Test Data Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Test Data Start from the root of tree.

10. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Apply Model to Test Data Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Test Data

11. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Apply Model to Test Data Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Test Data

12. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Apply Model to Test Data Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Test Data

13. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Apply Model to Test Data Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Test Data

14. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Apply Model to Test Data Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Test Data Assign Cheat to “No”

15. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Decision Tree Classification Task Decision Tree

16. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Decision Tree Induction o Many Algorithms: –Hunt’s Algorithm (one of the earliest) –CART –ID3, C4.5 –SLIQ,SPRINT

17. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 General Structure of Hunt’s Algorithm o Let D t be the set of training records that reach a node t o 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 ?

18. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 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

19. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Tree Induction o Greedy strategy. –Split the records based on an attribute test that optimizes certain criterion. o Issues 1.Determine how to split the records  How to specify the attribute test condition?  How to determine the best split? 2.Determine when to stop splitting

20. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Tree Induction o Greedy strategy. –Creates the tree top down starting from the root, and splits the records based on an attribute test that optimizes certain criterion. o 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

21. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 How to Specify Test Condition? o Depends on attribute types –Nominal –Ordinal –Continuous o Depends on number of ways to split –2-way split –Multi-way split

22. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Splitting Based on Nominal Attributes o Multi-way split: Use as many partitions as distinct values. o 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

23. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 o Multi-way split: Use as many partitions as distinct values. o Binary split: Divides values into two subsets. Need to find optimal partitioning. o 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}

24. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Splitting Based on Continuous Attributes o 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), clustering, or supervised clustering. –Binary Decision: (A < v) or (A  v)  consider all possible splits and finds the best cut v  can be more compute intensive

25. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Splitting Based on Continuous Attributes

26. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Tree Induction o Greedy strategy. –Split the records based on an attribute test that optimizes certain criterion. o 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

27. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 How to determine the Best Split Before Splitting: 10 records of class 0, 10 records of class 1 Which test condition is the best?

28. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 How to determine the Best Split o Greedy approach: –Nodes with homogeneous class distribution (pure nodes) are preferred o Need a measure of node impurity: Non-homogeneous, High degree of impurity Homogeneous, Low degree of impurity

29. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Measures of Node Impurity o Gini Index o Entropy o Misclassification error

30. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 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

31. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Alternative Splitting Criteria based on INFO o 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

32. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 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

33. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Splitting Based on INFO... o 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.

34. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Splitting Based on INFO... o 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

35. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Entropy and Gain Computations Assume we have m classes in our classification problem. A test S subdivides the examples D= (p 1,…,p m ) into n subsets D 1 =(p 11,…,p 1m ),…,D n =(p 11,…,p 1m ). The qualify of S is evaluated using Gain(D,S) (ID3) or GainRatio(D,S) (C5.0): Let H(D=(p 1,…,p m ))=  i=1 (p i log 2 (1/p i )) (called the entropy function) Gain(D,S)= H(D)   i=1 (|D i |/|D|)*H(D i ) Gain_Ratio(D,S)= Gain(D,S) / H(|D 1 |/|D|,…, |D n |/|D|) Remarks: |D| denotes the number of elements in set D. D=(p 1,…,p m ) implies that p 1 +…+ p m =1 and indicates that of the |D| examples p 1 *|D| examples belong to the first class, p 2 *|D| examples belong to the second class,…, and p m *|D| belong the m-th (last) class. H(0,1)=H(1,0)=0; H(1/2,1/2)=1, H(1/4,1/4,1/4,1/4)=2, H(1/p,…,1/p)=log 2 (p). C5.0 selects the test S with the highest value for Gain_Ratio(D,S), whereas ID3 picks the test S for the examples in set D with the highest value for Gain (D,S). m n

36. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Information Gain vs. Gain Ratio D=(2/3,1/3) D1(1,0)D2(1/3,2/3) D=(2/3,1/3) D1(0,1) D2(2/3,1/3) D3(1,0) D=(2/3,1/3) D1(1,0) D2(0,1) D3(1,0)D4(1,0)D5(1,0) D6(0,1) city=sf city=la car=merccar=taurus car=van age=22 age=25age=27age=35 age=40age=50 Gain(D,city=)= H(1/3,2/3) – ½ H(1,0) – ½ H(1/3,2/3)=0.45 Gain(D,car=)= H(1/3,2/3) – 1/6 H(0,1) – ½ H(2/3,1/3) – 1/3 H(1,0)=0.45 Gain(D,age=)= H(1/3,2/3) – 6*1/6 H(0,1) = 0.90 G_Ratio_pen(city=)=H(1/2,1/2)=1 G_Ratio_pen(age=)=log 2 (6)=2.58 G_Ratio_pen(car=)=H(1/2,1/3,1/6)=1.45 Result: I_Gain_Ratio: city>age>car Result: I_Gain: age > car=city

37. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Tree Induction o Greedy strategy. –Split the records based on an attribute test that optimizes certain criterion. o 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

38. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Stopping Criteria for Tree Induction o Stop expanding a node when all the records belong to the same class o Stop expanding a node when all the records have similar attribute values o Early termination (to be discussed later)

39. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Decision Tree Based Classification o 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 –Very good average performance over many datasets – If you want to show that your “new” classification technique really “improves the world”  compare its performance against decision trees (e.g. C 5.0)

40. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Example: C4.5 o Simple depth-first construction. o Uses Information Gain o Sorts Continuous Attributes at each node. o Needs entire data to fit in memory. o Unsuitable for Large Datasets. –Needs out-of-core sorting. o You can download the software from: http://www.cse.unsw.edu.au/~quinlan/c4.5r8.tar.gz http://www.cse.unsw.edu.au/~quinlan/c4.5r8.tar.gz

41. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Practical Issues of Classification o Underfitting and Overfitting o Missing Values o Costs of Classification

42. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Underfitting and Overfitting (Example) 500 circular and 500 triangular data points. Circular points: 0.5  sqrt(x 1 2 +x 2 2 )  1 Triangular points: sqrt(x 1 2 +x 2 2 ) > 0.5 or sqrt(x 1 2 +x 2 2 ) < 1

43. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Underfitting and Overfitting Overfitting Underfitting: when model is too simple, both training and test errors are large Complexity of a Decision Tree := number of nodes It uses Underfitting Complexity of the classification function

44. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Overfitting due to Noise Decision boundary is distorted by noise point

45. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Overfitting due to Insufficient Examples Lack of data points in the lower half of the diagram makes it difficult to predict correctly the class labels of that region - Insufficient number of training records in the region causes the decision tree to predict the test examples using other training records that are irrelevant to the classification task

46. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Notes on Overfitting o Overfitting results in decision trees that are more complex than necessary o Training error no longer provides a good estimate of how well the tree will perform on previously unseen records o Need new ways for estimating errors

47. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Occam’s Razor o Given two models of similar generalization errors, one should prefer the simpler model over the more complex model o For complex models, there is a greater chance that it was fitted accidentally by errors in data o Usually, simple models are more robust with respect to noise Therefore, one should include model complexity when evaluating a model

48. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Minimum Description Length (MDL) o Cost(Model,Data) = Cost(Data|Model) + Cost(Model) –Cost is the number of bits needed for encoding. –Search for the least costly model. o Cost(Data|Model) encodes the misclassification errors. o Cost(Model) uses node encoding (number of children) plus splitting condition encoding. Skip today, Read book

49. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 How to Address Overfitting o Pre-Pruning (Early Stopping Rule) –Stop the algorithm before it becomes a fully-grown tree –Typical stopping conditions for a node:  Stop if all instances belong to the same class  Stop if all the attribute values are the same –More restrictive conditions:  Stop if number of instances is less than some user-specified threshold  Stop if class distribution of instances are independent of the available features (e.g., using  2 test)  Stop if expanding the current node does not improve impurity measures (e.g., Gini or information gain).

50. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 How to Address Overfitting… o Post-pruning –Grow decision tree to its entirety –Trim the nodes of the decision tree in a bottom-up fashion –If generalization error improves after trimming, replace sub-tree by a leaf node. –Class label of leaf node is determined from majority class of instances in the sub-tree –Can use MDL for post-pruning

51. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Example of Post-Pruning Class = Yes20 Class = No10 Error = 10/30 Training Error (Before splitting) = 10/30 Pessimistic error = (10 + 0.5)/30 = 10.5/30 Training Error (After splitting) = 9/30 Pessimistic error (After splitting) = (9 + 4  0.5)/30 = 11/30 PRUNE! Class = Yes8 Class = No4 Class = Yes3 Class = No4 Class = Yes4 Class = No1 Class = Yes5 Class = No1

52. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Examples of Post-pruning –Optimistic error? –Pessimistic error? –Reduced error pruning? C0: 11 C1: 3 C0: 2 C1: 4 C0: 14 C1: 3 C0: 2 C1: 2 Don’t prune for both cases Don’t prune case 1, prune case 2 Case 1: Case 2: Depends on validation set

53. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Decision Boundary Border line between two neighboring regions of different classes is known as decision boundary Decision boundary is parallel to axes because test condition involves a single attribute at-a-time

54. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Oblique Decision Trees x + y < 1 Class = + Class = Test condition may involve multiple attributes More expressive representation Finding optimal test condition is computationally expensive

55. Tan,Steinbach, Kumar Introduction to Classification (with additions/modifications by Ch. Eick) 8/6/2005 Methods of Estimating Accuracy o Holdout –Reserve 2/3 for training and 1/3 for testing o Random subsampling –Repeated holdout o Cross validation –Partition data into k disjoint subsets –k-fold: train on k-1 partitions, test on the remaining one –Leave-one-out: k=n o Class stratified k-fold cross validation o Stratified sampling –oversampling vs undersampling Most popular!