Data Mining: Concepts and Techniques Chapter 4 (Introduction to Data Mining) Chapter 6 (Data Mining Concept and Analysis) Chapter 9 (Data Mining Analysis Fundamental Concept )

Classification and Prediction What is classification? What is prediction? Issues regarding classification and prediction Classification by decision tree induction Bayesian classification Rule-based classification Classification by back propagation Support Vector Machines (SVM) Associative classification Lazy learners (or learning from your neighbors) Other classification methods Prediction Accuracy and error measures Ensemble methods Model selection Summary

Classification vs. Prediction Given a collection of records (training set ) Each record is by characterized by a tuple (x,y), where x is the attribute set and y is the class label x: attribute, predictor, independent variable, input y: class, response, dependent variable, output Prediction models continuous-valued functions, i.e., predicts unknown or missing values

Examples of Classification Task Attribute set, x Class label, y Categorizing email messages Features extracted from email message header and content spam or non-spam Identifying tumor cells Features extracted from MRI scans malignant or benign cells Cataloging galaxies Features extracted from telescope images Elliptical, spiral, or irregular-shaped galaxies

Classification—A Two-Step Process Model construction: describing a set of predetermined classes Each tuple/sample is assumed to belong to a predefined class, as determined by the class label attribute The set of tuples used for model construction is training set The model is represented as classification rules, decision trees, or mathematical formulae Model usage: for classifying future or unknown objects Estimate accuracy of the model The known label of test sample is compared with the classified result from the model Accuracy rate is the percentage of test set samples that are correctly classified by the model Test set is independent of training set, otherwise over-fitting will occur If the accuracy is acceptable, use the model to classify data tuples whose class labels are not known

Process (1): Model Construction Classification Algorithms Training Data Classifier (Model) IF rank = ‘professor’ OR years > 6 THEN tenured = ‘yes’

Process (2): Using the Model in Prediction Classifier Testing Data Unseen Data (Jeff, Professor, 4) Tenured?

Classification Techniques Base Classifiers Decision Tree based Methods Rule-based Methods Nearest-neighbor Neural Networks Naïve Bayes and Bayesian Belief Networks Support Vector Machines Ensemble Classifiers Boosting, Bagging, Random Forests

Example of a Decision Tree categorical categorical continuous class Splitting Attributes Home Owner Yes No NO MarSt Single, Divorced Married Income NO < 80K > 80K NO YES Training Data Model: Decision Tree

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

Decision Tree Classification Task

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

Apply Model to Test Data Home Owner Yes No NO MarSt Single, Divorced Married Income NO < 80K > 80K NO YES

Apply Model to Test Data Home Owner Yes No NO MarSt Single, Divorced Married Income NO < 80K > 80K NO YES

Apply Model to Test Data Home Owner Yes No NO MarSt Single, Divorced Married Income NO < 80K > 80K NO YES

Apply Model to Test Data Home Owner Yes No NO MarSt Single, Divorced Married Income NO < 80K > 80K NO YES

Apply Model to Test Data Home Owner Yes No NO MarSt Single, Divorced Married Assign Defaulted to “No” Income NO < 80K > 80K NO YES

Supervised vs. Unsupervised Learning Supervised learning (classification) Supervision: The training data (observations, measurements, etc.) are accompanied by labels indicating the class of the observations New data is classified based on the training set Unsupervised learning (clustering) The class labels of training data is unknown Given a set of measurements, observations, etc. with the aim of establishing the existence of classes or clusters in the data

Chapter 6. Classification and Prediction What is classification? What is prediction? Issues regarding classification and prediction Classification by decision tree induction Bayesian classification Rule-based classification Classification by back propagation Support Vector Machines (SVM) Associative classification Lazy learners (or learning from your neighbors) Other classification methods Prediction Accuracy and error measures Ensemble methods Model selection Summary

Issues: Data Preparation Data cleaning Preprocess data in order to reduce noise and handle missing values Relevance analysis (feature selection) Remove the irrelevant or redundant attributes Data transformation Generalize and/or normalize data

Issues: Evaluating Classification Methods Accuracy classifier accuracy: predicting class label predictor accuracy: guessing value of predicted attributes Speed time to construct the model (training time) time to use the model (classification/prediction time) Robustness: handling noise and missing values Scalability: efficiency in disk-resident databases Interpretability understanding and insight provided by the model Other measures, e.g., goodness of rules, such as decision tree size or compactness of classification rules

Chapter 6. Classification and Prediction What is classification? What is prediction? Issues regarding classification and prediction Classification by decision tree induction Bayesian classification Rule-based classification Classification by back propagation Support Vector Machines (SVM) Associative classification Lazy learners (or learning from your neighbors) Other classification methods Prediction Accuracy and error measures Ensemble methods Model selection Summary

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

Decision Tree Induction: Training Dataset This follows an example of Quinlan’s ID3 (Playing Tennis)

Output: A Decision Tree for “buys_computer” age? overcast student? credit rating? <=30 >40 no yes 31..40 fair excellent

Algorithm for Decision Tree Induction Basic algorithm (a greedy algorithm) Tree is constructed in a top-down recursive divide-and-conquer manner At start, all the training examples are at the root Attributes are categorical (if continuous-valued, they are discretized in advance) Examples are partitioned recursively based on selected attributes Test attributes are selected on the basis of a heuristic or statistical measure (e.g., information gain) Conditions for stopping partitioning All samples for a given node belong to the same class There are no remaining attributes for further partitioning – majority voting is employed for classifying the leaf There are no samples left

Design Issues of Decision Tree Induction How should training records be split? Method for specifying test condition depending on attribute types Measure for evaluating the goodness of a test condition How should the splitting procedure stop? Stop splitting if all the records belong to the same class or have identical attribute values Early termination

Methods for Expressing Test Conditions Depends on attribute types Binary Nominal Ordinal Continuous Depends on number of ways to split 2-way split Multi-way split

Test Condition for Nominal Attributes Multi-way split: Use as many partitions as distinct values. Binary split: Divides values into two subsets Need to find optimal partitioning.

Test Condition for Ordinal Attributes Multi-way split: Use as many partitions as distinct values Binary split: Divides values into two subsets Need to find optimal partitioning Preserve order property among attribute values This grouping violates order property

Test Condition for Continuous Attributes

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

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

How to determine the Best Split Greedy approach: Nodes with purer class distribution are preferred Need a measure of node impurity: High degree of impurity Low degree of impurity

Measures of Node Impurity Gini Index Entropy Misclassification error

Finding the Best Split Compute impurity measure (P) before splitting Compute impurity measure (M) after splitting Compute impurity measure of each child node Compute the average impurity of the children (M) Choose the attribute test condition that produces the highest gain or equivalently, lowest impurity measure after splitting (M) Gain = P – M

Finding the Best Split P A? B? M11 M12 M21 M22 M1 M2 Before Splitting: P A? B? Yes No Yes No Node N1 Node N2 Node N3 Node N4 M11 M12 M21 M22 M1 M2 Gain = P – M1 vs P – M2

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

Computing Gini Index of a Single Node 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

Computing Gini Index for a Collection of Nodes When a node p is split into k partitions (children) where, ni = number of records at child i, n = number of records at parent node p. Choose the attribute that minimizes weighted average Gini index of the children Gini index is used in decision tree algorithms such as CART, SLIQ, SPRINT

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 – (1/6)2 = 0.278 Gini(N2) = 1 – (2/6)2 – (4/6)2 = 0.444 Gini(Children) = 6/12 * 0.278 + 6/12 * 0.444 = 0.361

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

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.

Continuous Attributes: Computing Gini Index... 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 Sorted Values Split Positions

GINI Index: CART CART: The CART measure is This measure thus prefers a split point that maximizes the difference between the class probability mass function for the two partitions; the higher the CART measure, the better the split point.

Measure of Impurity: Entropy Entropy at a given node t: (NOTE: p( j | t) is the relative frequency of class j at node t). Maximum (log nc) 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 quite similar to the GINI index computations

Computing Entropy of a Single Node 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) 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

Computing Information Gain After Splitting Parent Node, p is split into k partitions; ni is number of records in partition i Choose the split that achieves most reduction (maximizes GAIN) Used in the ID3 and C4.5 decision tree algorithms

Problems with Information Gain Info Gain tends to prefer splits that result in large number of partitions, each being small but pure Customer ID has highest information gain because entropy for all the children is zero

Gain Ratio Gain Ratio: Parent Node, p is split into k partitions ni 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 algorithm Designed to overcome the disadvantage of Information Gain

Measure of Impurity: Classification Error Classification error at a node t : 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

Computing Error of a Single Node 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

Comparing Attribute Selection Measures The three measures, in general, return good results but Information gain: biased towards multivalued attributes Gain ratio: tends to prefer unbalanced splits in which one partition is much smaller than the others Gini index: biased to multivalued attributes has difficulty when # of classes is large tends to favor tests that result in equal-sized partitions and purity in both partitions

Comparison among Impurity Measures For a 2-class problem:

Misclassification Error vs Gini Index Yes No Node N1 Node N2 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 but error remains the same!!

Decision Tree Based Classification 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

Other Attribute Selection Measures CHAID: a popular decision tree algorithm, measure based on χ2 test for independence C-SEP: performs better than info. gain and gini index in certain cases G-statistics: has a close approximation to χ2 distribution MDL (Minimal Description Length) principle (i.e., the simplest solution is preferred): The best tree as the one that requires the fewest # of bits to both (1) encode the tree, and (2) encode the exceptions to the tree Multivariate splits (partition based on multiple variable combinations) CART: finds multivariate splits based on a linear comb. of attrs. Which attribute selection measure is the best? Most give good results, none is significantly superior than others

Enhancements to Basic Decision Tree Induction Allow for continuous-valued attributes Dynamically define new discrete-valued attributes that partition the continuous attribute value into a discrete set of intervals Handle missing attribute values Assign the most common value of the attribute Assign probability to each of the possible values Attribute construction Create new attributes based on existing ones that are sparsely represented This reduces fragmentation, repetition, and replication

Classification in Large Databases Classification—a classical problem extensively studied by statisticians and machine learning researchers Scalability: Classifying data sets with millions of examples and hundreds of attributes with reasonable speed Why decision tree induction in data mining? relatively faster learning speed (than other classification methods) convertible to simple and easy to understand classification rules can use SQL queries for accessing databases comparable classification accuracy with other methods

Scalable Decision Tree Induction Methods SLIQ (EDBT’96 — Mehta et al.) Builds an index for each attribute and only class list and the current attribute list reside in memory SPRINT (VLDB’96 — J. Shafer et al.) Constructs an attribute list data structure PUBLIC (VLDB’98 — Rastogi & Shim) Integrates tree splitting and tree pruning: stop growing the tree earlier RainForest (VLDB’98 — Gehrke, Ramakrishnan & Ganti) Builds an AVC-list (attribute, value, class label) BOAT (PODS’99 — Gehrke, Ganti, Ramakrishnan & Loh) Uses bootstrapping to create several small samples