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Classification Classification vs. Prediction Classification: Prediction or Regression: predicts categorical class labels classifies data (constructs a model) based on the training set and the values (class labels) in a classifying attribute and uses it in classifying new data models continuous-valued functions, i.e., predicts unknown or missing values Typical Applications credit approval, target marketing, medical diagnosis treatment effectiveness analysis 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: 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 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 Classification Process (1): Model Construction Training Data NAME M ike M ary B ill Jim D ave A nne RANK YEARS TENURED A ssistant P rof 3 no A ssistant P rof 7 yes P rofessor 2 yes A ssociate P rof 7 yes A ssistant P rof 6 no A ssociate P rof 3 no Classification Algorithms Classifier (Model) IF rank = ‘professor’ OR years > 6 THEN tenured = ‘yes’ Classification Process (2): Use the Model in Prediction Classifier Testing Data Unseen Data (Jeff, Professor, 4) NAME T om M erlisa G eorge Joseph RANK YEARS TENURED A ssistant P rof 2 no A ssociate P rof 7 no P rofessor 5 yes A ssistant P rof 7 yes Tenured? 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 Important Issues Data cleaning Relevance analysis (feature selection) Remove the irrelevant or redundant attributes Data transformation Generalize and/or normalize data Accuracy Scalability Robustness Decision tree classifiers Widely used learning method Easy to interpret: can be re-represented as if-then-else rules Approximates function by piece wise constant regions Does not require any prior knowledge of data distribution, works well on noisy data. Setting Given old data about customers and payments, predict new applicant’s loan eligibility. Previous customers Age Salary Profession Location Customer type Classifier Decision rules Salary > 5 L Prof. = Exec New applicant’s data Good/ bad Decision trees Tree where internal nodes are simple decision rules on one or more attributes and leaf nodes are predicted class labels. Salary < 1 M Prof = teaching Good Bad Age < 30 Bad Good Training Dataset This follows an example from Quinlan’s ID3 age <=30 <=30 30…40 >40 >40 >40 31…40 <=30 <=30 >40 <=30 31…40 31…40 >40 income student credit_rating high no fair high no excellent high no fair medium no fair low yes fair low yes excellent low yes excellent medium no fair low yes fair medium yes fair medium yes excellent medium no excellent high yes fair medium no excellent buys_computer no no yes yes yes no yes no yes yes yes yes yes no Output: A Decision Tree for “buys_computer” age? <=30 student? overcast 30..40 yes >40 credit rating? no yes excellent fair no yes no yes Tree learning algorithms ID3 (Quinlan 1986) Successor C4.5 (Quinlan 1993) SLIQ (Mehta et al) SPRINT (Shafer et al) Basic algorithm for tree building Greedy top-down construction. Gen_Tree (Node, data) Stopping criteria make node a leaf? Yes Stop Selection Find best attribute and best split on attribute criteria Partition data on split condition For each child j of node Gen_Tree (node_j, data_j) Split criteria Select the attribute that is best for classification. Intuitively pick one that best separates instances of different classes. Quantifying the intuitive: measuring separability: First define impurity of an arbitrary set S consisting of K classes Information entropy: k Entropy( S ) pi log pi i 1 Zero when consisting of only one class, one when all classes in equal number. Information gain k Other measures of impurity: Gini: Gini 0 i 1 0.5 Entropy 1 Gini ( S ) 1 pi p1 0 1 1 Information gain on partitioning S into r subsets Impurity (S) - sum of weighted impurity of each subset r Gain( S , S1..S r ) Entropy( S ) j 1 Sj S Entropy( S j ) 2 Information Gain (ID3/C4.5) Select the attribute with the highest information gain Assume there are two classes, P and N Let the set of examples S contain p elements of class P and n elements of class N The amount of information, needed to decide if an arbitrary example in S belongs to P or N is defined as p p n n I ( p, n) log 2 log 2 pn pn pn pn Information Gain in Decision Tree Induction Assume that using attribute A a set S will be partitioned into sets {S1, S2 , …, Sv} If Si contains pi examples of P and ni examples of N, the entropy, or the expected information needed to classify objects in all subtrees Si is pi ni E ( A) I ( pi , ni ) i 1 p n The encoding information that would be gained by branching on A Gain( A) I ( p, n) E ( A) Attribute Selection by Information Gain Computation Class P: buys_computer = “yes” Class N: buys_computer = “no” I(p, n) = I(9, 5) =0.940 Compute the entropy for age: age <=30 30…40 >40 pi 2 4 3 ni I(pi, ni) 3 0.971 0 0 2 0.971 5 4 I ( 2,3) I ( 4,0) 14 14 5 I (3,2) 0.69 14 E ( age) Hence Gain(age) I ( p, n) E (age) Similarly Gain(income) 0.029 Gain( student ) 0.151 Gain(credit _ rating ) 0.048 Gini Index (IBM IntelligentMiner) If a data set T contains examples from n classes, gini index, n gini(T) is defined as gini(T ) 1 p 2 j 1 where pj is the relative frequency of class j in T. If a data set T is split into two subsets T1 and T2 with sizes N1 and N2 respectively, the gini index of the split data contains examples from n classes, the gini index gini(T) is defined as gini split (T ) j N 1 gini( ) N 2 gini( ) T1 T2 N N The attribute provides the smallest ginisplit(T) is chosen to split the node (need to enumerate all possible splitting points for each attribute). Extracting Classification Rules from Trees Represent the knowledge in the form of IF-THEN rules One rule is created for each path from the root to a leaf The leaf node holds the class prediction Example age = “<=30” AND student = “no” THEN buys_computer = “no” age = “<=30” AND student = “yes” THEN buys_computer = “yes” age = “31…40” THEN buys_computer = “yes” age = “>40” AND credit_rating = “excellent” THEN buys_computer = “yes” IF age = “>40” AND credit_rating = “fair” THEN buys_computer = “no” IF IF IF IF Avoid Overfitting in Classification The generated tree may overfit the training data Too many branches, some may reflect anomalies due to noise or outliers Result is in poor accuracy for unseen samples Two approaches to avoid overfitting Prepruning: Halt tree construction early—do not split a node if this would result in the goodness measure falling below a threshold Postpruning: Remove branches from a “fully grown” tree—get a sequence of progressively pruned trees Use a set of data different from the training data to decide which is the “best pruned tree” Classification in Large Databases 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