Classification and Regression

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1 Classification and Regression

2 Announcements Study guide for exam is on the LMS Sample exam will be posted by Monday Reminder that phase 3 oral presentations are being held next week during workshops

3 Plan Today Decision tree classification Brief recap: k nearest neighbor classification Next week Monday Correlation and classification: putting it together Demo of recurrent neural networks and Chinese folk music composition. Can you identify the computer composition from a human composition?

4 Classification and Regression What is Classification and Regression? Classification algorithms: K-Nearest Neighbor Classifier (K-NN) Decision tree

5 Classification Predicting disease from microarray data Gene 1 Gene 2 Gene 3 Gene n Person Person Person Person m Cancer Test data Gene 1 Gene 2 Gene 3 Gene n Cancer Person m ?

6 Classification example Animal classification Test data

7 Classification example Banking: classifying borrower Test data Tid Home Owner Marital status Annual Income Defaulted Borrower 11 No Single 55K?

8 10 Classification example Detecting tax fraud Test data Tid Refund Marital Status Taxable Income 1 Yes Single 125K No 2 No Married 100K No 3 No Single 70K No 4 Yes Married 120K No Cheat 5 No Divorced 95K Yes 6 No Married 60K No 7 Yes Divorced 220K No 8 No Single 85K Yes 9 No Married 75K No 10 No Single 90K Yes Tid Refund Marital Status Taxable Income 11 Yes Married 125K? Cheat

9 More 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

10 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. y = f(x 1, x 2,, x n ) y: discrete value, target variable x 1, x n : attributes, predictors 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.

11 Classification framework

12 Regression Given a collection of records (training set ) Each record contains a set of attributes, one of the attributes is the target variable. Learn predictive model from data y = f(x 1, x 2,, x n ) y: continuous real value, target variable x 1, x n : attributes, predictors

13 Regression Predicting ice-creams consumption from temperature: y = f(x)

14 Regression Predicting ice-creams consumption from temperature: y = f(x)?

15 Regression Stock market prediction x(t) = f(x(t-1), x(t-2), )

16 Regression Predicting activity level of a target gene Gene 1 Gene 2 Gene 3 Gene n Person Person Person Person m Gene n Gene 1 Gene 2 Gene 3 Gene n Gene n+1 Person m ?

17 Classification and Regression What is Classification and Regression? Classification algorithms: K-Nearest Neighbor Classifier (K-NN) Decision tree Others Random Forest Deep neural network

18 Classification algorithms K-Nearest Neighbor Classifier (K-NN) Decision tree Others Random Forest Deep neural network

19 Nearest Neighbor Classifiers Basic idea: If it walks like a duck, quacks like a duck, then it s probably a duck Compute Distance Test Record Training Records Choose k of the nearest records

20 Nearest-Neighbor Classifiers Unknown record Requires three things The set of stored records Distance Metric to compute distance between records The value of k, the number of nearest neighbors to retrieve To classify an unknown record: 1. Compute distance to other training records 2. Identify k nearest neighbors 3. Use class labels of nearest neighbors to determine the class label of unknown record (e.g., by taking majority vote)

21 Definition of Nearest Neighbor X X X (a) 1-nearest neighbor (b) 2-nearest neighbor (c) 3-nearest neighbor K-nearest neighbors of a record x are data points that have the k smallest distance to x

22 Distance measure Compute distance between two points: Euclidean distance d( p, q) = i ( p q i i ) 2 Pearson coefficient (similarity measure) Determine the class from nearest neighbor list take the majority vote of class labels among the k- nearest neighbors Weigh the vote according to distance weight factor, w = 1/d 2

23 1 nearest-neighbor Voronoi Diagram defines the classification boundary The area takes the class of the green point

24 K- Nearest Neighbor classifier Choosing the value of k: If k is too small, sensitive to noise points If k is too large, neighborhood may include points from other classes X

25 K-NN classifier Lazy learning: we don t learn any model Need to store some data Distance function: Euclidean Pearson coefficient K-NN classifier model K: number of neighbors Challenges: Large number of points: storage cost, nearest neighbor search cost

26 K-NN classifier: parameter tuning Parameters: K: number of neighbors Distance metric Divide training data into: Training subset Validation subset Train models on the training subset Evaluate performance on the validation subset

27 Metrics for Performance Evaluation Can be summarized in a Confusion Matrix (contingency table) Actual class: {yes, no, yes, yes, } Predicted class: {no, yes, yes, no } ACTUAL CLASS PREDICTED CLASS Class=Yes Class=No Class=Yes a b Class=No c d a: TP (true positive) b: FN (false negative) c: FP (false positive) d: TN (true negative)

28 Metrics for Performance Evaluation PREDICTED CLASS Class=Yes Class=No ACTUAL CLASS Class=Yes Class=No a (TP) c (FP) b (FN) d (TN) Most widely-used metric: a + d TP + TN Accuracy = = a + b + c + d TP + TN + FP Others: precision, recall, F1-score + FN

29 Accuracy Actual class: Predicted: {yes, no, yes, yes, no, yes, no, no} {no, yes, yes, no, yes, no, no, yes} Accuracy? TP TN FP FN

30 Actual class: Predicted: {yes, no, yes, yes, no, yes, no, no} {no, yes, yes, no,yes, no, no, yes} PREDICTED CLASS Class=Yes Class=No ACTUAL CLASS Class=Yes a= 1 (TP) Class=No c=3 (FP) b=3 (FN) d=1 (TN)

31 Metrics for Performance Evaluation: Multiple-class classification Actual class: {1, 1, 2, 3, } Predicted class: {3, 1, 2, 1, } PREDICTED CLASS Class 1 Class 2 Class 3 ACTUAL CLASS Class Class Class

32 Classification algorithms K-Nearest Neighbor Classifier (K-NN) Decision tree Others: Random Forest Deep neural network

33 10 Example of a Decision Tree Tid Refund Marital Status Taxable Income Cheat Splitting Attributes 1 Yes Single 125K No 2 No Married 100K No 3 No Single 70K No 4 Yes Married 120K No 5 No Divorced 95K Yes 6 No Married 60K No 7 Yes Divorced 220K No 8 No Single 85K Yes 9 No Married 75K No 10 No Single 90K Yes Refund Yes No NO MarSt Single, Divorced TaxInc < 80K > 80K NO YES Married NO Training Data Model: Decision Tree

34 10 Another Example of Decision Tree Tid Refund Marital Status Taxable Income 1 Yes Single 125K No 2 No Married 100K No 3 No Single 70K No 4 Yes Married 120K No Cheat 5 No Divorced 95K Yes 6 No Married 60K No 7 Yes Divorced 220K No 8 No Single 85K Yes 9 No Married 75K No 10 No Single 90K Yes Married NO MarSt Yes NO Single, Divorced Refund NO No TaxInc < 80K > 80K YES There could be more than one tree that fits the same data!

35 10 10 Decision Tree Classification Task Tid Attrib1 Attrib2 Attrib3 Class 1 Yes Large 125K No 2 No Medium 100K No 3 No Small 70K No 4 Yes Medium 120K No 5 No Large 95K Yes 6 No Medium 60K No 7 Yes Large 220K No 8 No Small 85K Yes 9 No Medium 75K No 10 No Small 90K Yes Training Set Tid Attrib1 Attrib2 Attrib3 Class 11 No Small 55K? 12 Yes Medium 80K? 13 Yes Large 110K? 14 No Small 95K? 15 No Large 67K? Test Set Induction Deduction Tree Induction algorithm Learn Model Apply Model Model Decision Tree

36 10 Apply Model to Test Data Start from the root of tree. Test Data Refund Marital Status Taxable Income Cheat Yes Refund No No Married 80K? NO Single, Divorced MarSt Married TaxInc < 80K > 80K NO NO YES

37 10 Apply Model to Test Data Test Data Refund Marital Status Taxable Income Cheat Yes Refund No No Married 80K? NO Single, Divorced MarSt Married TaxInc < 80K > 80K NO NO YES

38 10 Apply Model to Test Data Test Data Refund Marital Status Taxable Income Cheat Yes Refund No No Married 80K? NO Single, Divorced MarSt Married TaxInc < 80K > 80K NO NO YES

39 10 Apply Model to Test Data Test Data Refund Marital Status Taxable Income Cheat Yes Refund No No Married 80K? NO Single, Divorced MarSt Married TaxInc < 80K > 80K NO NO YES

40 10 Apply Model to Test Data Test Data Refund Marital Status Taxable Income Cheat Yes Refund No No Married 80K? NO Single, Divorced MarSt Married TaxInc < 80K > 80K NO NO YES

41 10 Apply Model to Test Data Test Data Refund Marital Status Taxable Income Cheat Refund No Married 80K? Yes No NO Single, Divorced MarSt Married Assign Cheat to No TaxInc NO < 80K > 80K NO YES

42 10 Apply Model to Test Data Start from the root of tree. Test Data Refund Marital Status Taxable Income Cheat Yes Refund No No Single 100K? NO Single, Divorced MarSt Married TaxInc < 80K > 80K NO NO YES

43 Decision Trees Decision tree A flow-chart-like tree structure Internal node denotes a test on an attribute Branch represents an outcome of the test Leaf nodes represent class labels or class distribution

44 10 10 Decision Tree Classification Task Tid Attrib1 Attrib2 Attrib3 Class 1 Yes Large 125K No 2 No Medium 100K No 3 No Small 70K No 4 Yes Medium 120K No 5 No Large 95K Yes 6 No Medium 60K No 7 Yes Large 220K No 8 No Small 85K Yes 9 No Medium 75K No 10 No Small 90K Yes Training Set Tid Attrib1 Attrib2 Attrib3 Class 11 No Small 55K? 12 Yes Medium 80K? 13 Yes Large 110K? 14 No Small 95K? 15 No Large 67K? Test Set Induction Deduction Tree Induction algorithm Learn Model Apply Model Model Decision Tree

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

46 10 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 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. Tid Refund Marital Status Taxable Income 1 Yes Single 125K No 2 No Married 100K No 3 No Single 70K No 4 Yes Married 120K No Cheat 5 No Divorced 95K Yes 6 No Married 60K No 7 Yes Divorced 220K No 8 No Single 85K Yes 9 No Married 75K No 10 No Single 90K Yes D t Refund Yes No

47 10 Example 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. Tid Refund Marital Status Taxable Income 1 Yes Single 125K No 2 No Married 100K No 3 No Single 70K No 4 Yes Married 120K No Cheat 5 No Divorced 95K Yes 6 No Married 60K No 7 Yes Divorced 220K No 8 No Single 85K Yes 9 No Married 75K No 10 No Single 90K Yes D t Refund Yes No

48 Stopping condition: leaf node 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 Refund Yes No

49 Splitting Attributes Yes Refund No NO Single, Divorced MarSt Married TaxInc < 80K > 80K NO NO YES Model: Decision Tree

50 Tree Induction 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

51 Tree Induction 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

52 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

53 Splitting Based on Nominal Attributes Multi-way split: Use as many partitions as distinct values. Family CarType Sports Luxury Binary split: Divides values into two subsets. Need to find optimal partitioning. {Sports, Luxury} CarType {Family} OR {Family, Luxury} CarType {Sports}

54 Splitting Based on Ordinal Attributes Multi-way split: Use as many partitions as distinct values. Small Size Medium Large Binary split: Divides values into two subsets. Need to find optimal partitioning. {Small, Medium} Size {Large} OR {Medium, Large} Size {Small} What about this split? {Small, Large} Size {Medium}

55 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

56 Splitting Based on Continuous Attributes Taxable Income > 80K? Taxable Income? < 10K > 80K Yes No [10K,25K) [25K,50K) [50K,80K) (i) Binary split (ii) Multi-way split

57 Tree Induction 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

58 How to determine the Best Split Before Splitting: 10 records of class 0, 10 records of class 1 Own Car? Car Type? Student ID? Yes No Family Luxury c 1 c 10 c 20 Sports c 11 C0: 6 C1: 4 C0: 4 C1: 6 C0: 1 C1: 3 C0: 8 C1: 0 C0: 1 C1: 7 C0: 1 C1: 0... C0: 1 C1: 0 C0: 0 C1: 1... C0: 0 C1: 1 Which test condition is the best?

59 How to determine the Best Split Greedy approach: Nodes with homogeneous class distribution are preferred Need a measure of node impurity: C0: 5 C1: 5 Non-homogeneous, High degree of impurity C0: 9 C1: 1 Homogeneous, Low degree of impurity

60 Measures of Node Impurity Misclassification error We are not going to cover --- skip Entropy

61 Node Impurity Criteria based on Entropy Entropy at a given node t: Entropy ( t) = p( j t)log p( j t) j (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 Minimum (0.0) when all records belong to one class

62 Examples for computing Entropy Entropy t) = p( j t)log p( j t) j ( 2 C1 0 C2 6 P(C1) = 0/6 = 0 P(C2) = 6/6 = 1 Entropy = 0 log 0 1 log 1 = 0 0 = 0 C1 1 C2 5 P(C1) = 1/6 P(C2) = 5/6 Entropy = (1/6) log 2 (1/6) (5/6) log 2 (1/6) = 0.65 C1 2 C2 4?

63 Examples for computing Entropy Entropy t) = p( j t)log p( j t) j ( 2 C1 0 C2 6 P(C1) = 0/6 = 0 P(C2) = 6/6 = 1 Entropy = 0 log 0 1 log 1 = 0 0 = 0 C1 1 C2 5 P(C1) = 1/6 P(C2) = 5/6 Entropy = (1/6) log 2 (1/6) (5/6) log 2 (1/6) = 0.65 C1 2 C2 4 P(C1) = 2/6 P(C2) = 4/6 Entropy = (2/6) log 2 (2/6) (4/6) log 2 (4/6) = 0.92

64 How good is a Split? Compare the impurity of parent node (before splitting) With the impurity of the children nodes (after splitting) I(v j ): impurity measure of node v j j: children node index N(v j ): number of data points in child node v j N: number of data points in parent node The larger the gain, the better

65 How good is a Split? For I(v) being the entropy function: Information gain Where I() is the entropy function H() Note: the information gain is equivalent to the mutual information between the class variable and the test attribute Thus splitting using the information gain is to choose the attribute with highest information shared with the class variable

66 How to determine the Best Split? Before Splitting: 10 records of class 0, 10 records of class 1 Own Car? Car Type? Student ID? Yes No Family Luxury c 1 c 10 c 20 Sports c 11 C0: 6 C1: 4 C0: 4 C1: 6 C0: 1 C1: 3 C0: 8 C1: 0 C0: 1 C1: 7 C0: 1 C1: 0... C0: 1 C1: 0 C0: 0 C1: 1... C0: 0 C1: 1 Which test condition is the best? - Compute the gain of all splits - Choose the one with largest gain

67 Others Random Forest: Community of Experts Train multiple decision trees on random subsets of samples Decision via majority voting

68 Deep neural networks Mimic the biological brain State of the art classifiers for images and speech data

69 References and Acknowledgement This lecture was prepared using some material adapted from: CS059 - Data Mining -- Slides chap4_basic_classification.ppt

70 Next week Next week Monday Correlation and classification: putting it together Demo of recurrent neural networks and Chinese folk music composition. Can you identify the computer composition from a human composition? Phase 3 oral presentations during workshops

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