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Data Mining Classification: Basic Concepts, Decision Trees, and Model Evaluation

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  1. Data Mining Classification: Basic Concepts, Decision Trees, and Model Evaluation Lecture Notes for Chapter 3

  2. Why Data Mining • Credit ratings/targeted marketing: • Given a database of 100,000 names, which persons are the least likely to default on their credit cards? • Identify likely responders to sales promotions • Fraud detection • Which types of transactions are likely to be fraudulent, given the demographics and transactional history of a particular customer? • Customer relationship management: • Which of my customers are likely to be the most loyal, and which are most likely to leave for a competitor? : Data Mining helps extract such information

  3. 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

  4. Applications • Banking: loan/credit card approval • predict good customers based on old customers • Customer relationship management: • identify those who are likely to leave for a competitor. • Targeted marketing: • identify likely responders to promotions • Fraud detection: telecommunications, financial transactions • from an online stream of event identify fraudulent events • Manufacturing and production: • automatically adjust knobs when process parameter changes

  5. 4.1 Preliminary MODELING PROCESS CLASSIFICATION MODEL OUTPUT CLASS LABEL Y INPUT ATTRIBUTE SET X

  6. 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.

  7. * Purposes • Descriptive modeling • To have descriptive model that explains and distinguishes between objects of different classes. • Predictive Modeling • Predict class label of (new) unknown records. To automatically assigns a class label when presented with the attribute set of an unknown record.

  8. * Predictive modeling

  9. * classification • ดีกับ • Predict, describe data sets ที่เป็น binary or nominal categories • ไม่ค่อยดีกับ • Ordinal categories เพราะไม่สามารถพิจารณาลำดับได้ • ลำดับขั้น เช่นมนุษย์ สัตว์เลือดอุ่น

  10. * 4.2 Approach to solving a classification problem • แต่ละเทคนิคจะใช้ Learning algorithm ที่แตกต่างกันไปเพื่อสร้างตัวแบบที่ best fit กับ relationship ระหว่าง attribute set กับ class label ที่ให้มาจาก input data • จุดหมายคือ สร้างให้ถูกต้องสำหรับแต่ละ record ของ train และ test sets และถูกต้องกับข้อมูลทั่วไปหรือ unseen records

  11. * วัดความถูกต้อง • ให้ fijแทนจำนวน obj ที่ actual class i และ predicted class j • Accuracy = (#correct predictions) / (#total predictions) • = (f11 + f00)/(f11 + f10 + f01 + f00) • Error rate = (#wrong predictions) / (#total predictions) • = (f10 + f01)/(f11 + f10 + f01 + f00)

  12. Illustrating Classification Task

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

  14. *4.3 Decision tree generation Decision tree: • Root node has no incoming edges and zero or more outgoing edges (condition att) • Internal node has exactly one incoming edge and two or more outgoing edges (condition att) • Leaf or terminal nodes have exactly one incoming edge and no outgoing edges (for class label)

  15. 4.3.1 How a decision tree works

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

  17. NO Another Example of Decision Tree categorical categorical continuous class Single, Divorced MarSt Married NO Refund No Yes TaxInc < 80K > 80K YES NO There could be more than one tree that fits the same data! (exponential no.) ทำได้แค่สร้างต้นไม้ที่ถูกต้องเกือบ optimal หรือแค่ ใช้เวลาไม่มากเกินไป

  18. Decision Tree Classification Task Decision Tree

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

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

  21. Decision Tree Classification Task Decision Tree

  22. 4.3.2 Decision Tree Induction • Many Algorithms: • Hunt’s Algorithm (one of the earliest) • CART • ID3, C4.5 • SLIQ,SPRINT Hunt’s algo เป็นวิธีแบบ recursive ที่ partition training records ให้ได้เป็น subsets ที่ pure ขึ้น

  23. General Structure of Hunt’s Algorithm • Let Dt be the set of training records that reach a node t • General Procedure: • If Dt contains records that belong the same class yt, then t is a leaf node labeled as yt • If Dt is an empty set, then t is a leaf node labeled by the default class, yd • If Dt 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. Dt ?

  24. Refund Refund Yes No Yes No Don’t Cheat Marital Status Don’t Cheat Marital Status Single, Divorced Refund Married Married Single, Divorced Yes No Don’t Cheat Taxable Income Cheat Don’t Cheat Don’t Cheat Don’t Cheat < 80K >= 80K Don’t Cheat Cheat Hunt’s Algorithm Default = no Don’t Cheat

  25. 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 • เมื่อทุก records ตกอยู่ที่ class ต่าง ๆ หมด?

  26. 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

  27. How to Specify Test Condition? • Depends on attribute types • Nominal • Ordinal • Continuous • Depends on number of ways to split • 2-way split (ถ้าเป็น binary ก็อย่างนี้อยู่แล้ว) • Multi-way split

  28. CarType Family Luxury Sports CarType CarType {Sports, Luxury} {Family, Luxury} {Family} {Sports} 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. OR แบบ binary split ถ้ามี k attributes จะ split ได้กี่แบบ? 2k-1 – 1 แบบ

  29. Size Small Large Medium Size Size Size {Small, Medium} {Small, Large} {Medium, Large} {Medium} {Large} {Small} Splitting Based on Ordinal Attributes • 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? OR

  30. 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

  31. Splitting Based on Continuous Attributes vi =< A < vi+1 , i = 1, 2, …, k

  32. 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

  33. How to determine the Best Split Before Splitting: 10 records of class 0, 10 records of class 1 Purer! Which test condition is the best?

  34. 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

  35. Measures of Node Impurity • Gini Index • Entropy • Misclassification error • ทั้งสามอย่างวัด impurity ยิ่งมากยิ่งไม่ดี เช่น (0,1) จะมี zero impurity แต่ (0.5, 0.5) จะมี highest impurity

  36. M0 M2 M3 M4 M1 M12 M34 How to Find the Best Split Before Splitting: A? B? Yes No Yes No Node N1 Node N2 Node N3 Node N4 Gain = M0 – M12 vs M0 – M34

  37. Measure of Impurity: GINI • Gini Index for a given node t : (NOTE: p( j | t) or pi is the relative frequency of class j at node t, c เป็นจำนวน classes). • Maximum (1 - 1/nc) when records are equally distributed among all classes, implying least interesting information • Minimum (0) when all records belong to one class, implying most interesting information

  38. 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 = 0.278 P(C1) = 2/6 P(C2) = 4/6 Gini = 1 – (2/6)2 – (4/6)2 = 0.444

  39. Splitting Based on GINI การตัดสินใจว่าจะ split att ไหนก่อน จะต้องเปรียบเทียบค่า GINI ระหว่าง parent node (ก่อน split) กับ child node (หลัง split) ยิ่งผลต่างหรือที่เรียกว่า Gain ต่างกันเท่าไหร่ก็แสดงว่า att นั้นดีสุด • Used in CART, SLIQ, SPRINT. • When a node p is split into k partitions (children), the quality of split is computed as, Gain = 1 - Ginisplit where, ni = number of records at child i, n = number of records at node p.

  40. Binary Attributes: Computing GINI Index • Splits into two partitions • Effect of Weighing partitions: • Larger and Purer Partitions are sought for. B? Yes No Node N1 Node N2 Gini(N1) = 1 – (5/6)2 – (2/6)2= 0.194 Gini(N2) = 1 – (1/6)2 – (4/6)2= 0.528 Gini(Children) = 7/12 * 0.194 + 5/12 * 0.528= 0.333 แสดงว่าควร split ที่ B

  41. Categorical Attributes: Computing Gini Index • For each distinct value, gather counts for each class in the dataset • Use the count matrix to make decisions Two-way split (find best partition of values) Multi-way split Gini({spo,Lux})=1 – 3/52 - 2/52 = 0.48 Gini({family}) = 1 – 1/52 - 4/52 = 0.32 GINIsplit = (5/20)*.48 +(5/20)*0.32 =0.2 ดีกว่า

  42. Continuous Attributes: Computing Gini Index • Use Binary Decisions based on one value • Several Choices for the splitting value • Number of possible splitting values = Number of distinct values • Each splitting value has a count matrix associated with it • Class counts in each of the partitions, A < v and A  v • Simple method to choose best v • For each v, scan the database to gather count matrix and compute its Gini index • Computationally Inefficient! Repetition of work. • วิธีนี้สำหรับ N records ต้องใช้ O(N) และคำนวณ GINI ใช้ O(N) จึงต้องใช้รวมกัน O(N2)

  43. Sorted Values Split Positions Continuous Attributes: Computing Gini Index • ใช้แค่ O(NlogN) • For efficient computation: for each attribute, • Sort the attribute on values • Linearly scan these values, each time updating the count matrix and computing Gini index • Choose the split position that has the least Gini index

  44. A? Yes No Node N1 Node N2 Gini Gini(N1) = 1 – (3/3)2 – (0/3)2= 0 Gini(N2) = 1 – (4/7)2 – (3/7)2= 0.489 Gini(Children) = 3/10 * 0 + 7/10 * 0.489= 0.342 Gini improves !! แสดงว่าควร split ที่ A

  45. Alternative Splitting Criteria based on INFO • 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 nc) when records are equally distributed among all classes implying least information • Minimum (0) when all records belong to one class, implying most information • Entropy based computations are similar to the GINI index computations

  46. Examples for computing Entropy P(C1) = 0/6 = 0 P(C2) = 6/6 = 1 Entropy = – 0 log 0– 1 log 1 = – 0 – 0 = 0 ดีสุด P(C1) = 1/6 P(C2) = 5/6 Entropy = – (1/6) log2 (1/6)– (5/6) log2 (1/6) = 0.65 P(C1) = 2/6 P(C2) = 4/6 Entropy = – (2/6) log2 (2/6)– (4/6) log2 (4/6) = 0.92 แย่สุด

  47. Splitting Based on INFO... • Information Gain: Parent Node, p is split into k partitions; ni 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