Chapter 8. Classification Basic Concepts.ppt

1 Data Mining: Concepts and Techniques (3rd ed.) Chapter 8 Subrata Kumer Paul Assistant Professor, Dept. of CSE, BAUET sksubrata96@gmail.com

3 Chapter 8. Classification: Basic Concepts  Classification: Basic Concepts  Decision Tree Induction  Bayes Classification Methods  Rule-Based Classification  Model Evaluation and Selection  Techniques to Improve Classification Accuracy: Ensemble Methods  Summary

4 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

5  Classification  predicts categorical class labels (discrete or nominal)  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  Numeric Prediction  models continuous-valued functions, i.e., predicts unknown or missing values  Typical applications  Credit/loan approval:  Medical diagnosis: if a tumor is cancerous or benign  Fraud detection: if a transaction is fraudulent  Web page categorization: which category it is Prediction Problems: Classification vs. Numeric Prediction

6 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 overfitting)  If the accuracy is acceptable, use the model to classify new data  Note: If the test set is used to select models, it is called validation (test) set

7 Process (1): Model Construction Training Data NAME RANK YEARS TENURED Mike Assistant Prof 3 no Mary Assistant Prof 7 yes Bill Professor 2 yes Jim Associate Prof 7 yes Dave Assistant Prof 6 no Anne Associate Prof 3 no Classification Algorithms IF rank = ‘professor’ OR years > 6 THEN tenured = ‘yes’ Classifier (Model)

8 Process (2): Using the Model in Prediction Classifier Testing Data NAME RANK YEARS TENURED Tom Assistant Prof 2 no Merlisa Associate Prof 7 no George Professor 5 yes Joseph Assistant Prof 7 yes Unseen Data (Jeff, Professor, 4) Tenured?

10 Decision Tree Induction: An Example age? overcast student? credit rating? <=30 >40 no yes yes yes 31..40 fair excellent yes no age income student credit_rating buys_computer <=30 high no fair no <=30 high no excellent no 31…40 high no fair yes >40 medium no fair yes >40 low yes fair yes >40 low yes excellent no 31…40 low yes excellent yes <=30 medium no fair no <=30 low yes fair yes >40 medium yes fair yes <=30 medium yes excellent yes 31…40 medium no excellent yes 31…40 high yes fair yes >40 medium no excellent no  Training data set: Buys_computer  The data set follows an example of Quinlan’s ID3 (Playing Tennis)  Resulting tree:

11 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

Brief Review of Entropy  12 m = 2

13 Attribute Selection Measure: Information Gain (ID3/C4.5)  Select the attribute with the highest information gain  Let pi be the probability that an arbitrary tuple in D belongs to class Ci, estimated by |Ci, D|/|D|  Expected information (entropy) needed to classify a tuple in D:  Information needed (after using A to split D into v partitions) to classify D:  Information gained by branching on attribute A ) ( log ) ( 2 1 i m i i p p D Info     ) ( | | | | ) ( 1 j v j j A D Info D D D Info     (D) Info Info(D) Gain(A) A  

14 Attribute Selection: Information Gain  Class P: buys_computer = “yes”  Class N: buys_computer = “no” means “age <=30” has 5 out of 14 samples, with 2 yes’es and 3 no’s. Hence Similarly, age pi ni I(pi, ni) <=30 2 3 0.971 31…40 4 0 0 >40 3 2 0.971 694 . 0 ) 2 , 3 ( 14 5 ) 0 , 4 ( 14 4 ) 3 , 2 ( 14 5 ) (     I I I D Infoage 048 . 0 ) _ ( 151 . 0 ) ( 029 . 0 ) (    rating credit Gain student Gain income Gain 246 . 0 ) ( ) ( ) (    D Info D Info age Gain age age income student credit_rating buys_computer <=30 high no fair no <=30 high no excellent no 31…40 high no fair yes >40 medium no fair yes >40 low yes fair yes >40 low yes excellent no 31…40 low yes excellent yes <=30 medium no fair no <=30 low yes fair yes >40 medium yes fair yes <=30 medium yes excellent yes 31…40 medium no excellent yes 31…40 high yes fair yes >40 medium no excellent no ) 3 , 2 ( 14 5 I 940 . 0 ) 14 5 ( log 14 5 ) 14 9 ( log 14 9 ) 5 , 9 ( ) ( 2 2      I D Info

15 Computing Information-Gain for Continuous-Valued Attributes  Let attribute A be a continuous-valued attribute  Must determine the best split point for A  Sort the value A in increasing order  Typically, the midpoint between each pair of adjacent values is considered as a possible split point  (ai+ai+1)/2 is the midpoint between the values of ai and ai+1  The point with the minimum expected information requirement for A is selected as the split-point for A  Split:  D1 is the set of tuples in D satisfying A ≤ split-point, and D2 is the set of tuples in D satisfying A > split-point

16 Gain Ratio for Attribute Selection (C4.5)  Information gain measure is biased towards attributes with a large number of values  C4.5 (a successor of ID3) uses gain ratio to overcome the problem (normalization to information gain)  GainRatio(A) = Gain(A)/SplitInfo(A)  Ex.  gain_ratio(income) = 0.029/1.557 = 0.019  The attribute with the maximum gain ratio is selected as the splitting attribute ) | | | | ( log | | | | ) ( 2 1 D D D D D SplitInfo j v j j A     

17 Gini Index (CART, IBM IntelligentMiner)  If a data set D contains examples from n classes, gini index, gini(D) is defined as where pj is the relative frequency of class j in D  If a data set D is split on A into two subsets D1 and D2, the gini index gini(D) is defined as  Reduction in Impurity:  The attribute provides the smallest ginisplit(D) (or the largest reduction in impurity) is chosen to split the node (need to enumerate all the possible splitting points for each attribute)     n j p j D gini 1 2 1 ) ( ) ( | | | | ) ( | | | | ) ( 2 2 1 1 D gini D D D gini D D D giniA   ) ( ) ( ) ( D gini D gini A gini A   

18 Computation of Gini Index  Ex. D has 9 tuples in buys_computer = “yes” and 5 in “no”  Suppose the attribute income partitions D into 10 in D1: {low, medium} and 4 in D2 Gini{low,high} is 0.458; Gini{medium,high} is 0.450. Thus, split on the {low,medium} (and {high}) since it has the lowest Gini index  All attributes are assumed continuous-valued  May need other tools, e.g., clustering, to get the possible split values  Can be modified for categorical attributes 459 . 0 14 5 14 9 1 ) ( 2 2                 D gini ) ( 14 4 ) ( 14 10 ) ( 2 1 } , { D Gini D Gini D gini medium low income               

19 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

20 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-statistic: 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

21 Overfitting and Tree Pruning  Overfitting: An induced tree may overfit the training data  Too many branches, some may reflect anomalies due to noise or outliers  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  Difficult to choose an appropriate 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”

22 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

23 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 is decision tree induction popular?  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  RainForest (VLDB’98 — Gehrke, Ramakrishnan & Ganti)  Builds an AVC-list (attribute, value, class label)

24 Scalability Framework for RainForest  Separates the scalability aspects from the criteria that determine the quality of the tree  Builds an AVC-list: AVC (Attribute, Value, Class_label)  AVC-set (of an attribute X )  Projection of training dataset onto the attribute X and class label where counts of individual class label are aggregated  AVC-group (of a node n )  Set of AVC-sets of all predictor attributes at the node n

25 Rainforest: Training Set and Its AVC Sets student Buy_Computer yes no yes 6 1 no 3 4 Age Buy_Computer yes no <=30 2 3 31..40 4 0 >40 3 2 Credit rating Buy_Computer yes no fair 6 2 excellent 3 3 age income studentcredit_rating buys_computer <=30 high no fair no <=30 high no excellent no 31…40 high no fair yes >40 medium no fair yes >40 low yes fair yes >40 low yes excellent no 31…40 low yes excellent yes <=30 medium no fair no <=30 low yes fair yes >40 medium yes fair yes <=30 medium yes excellent yes 31…40 medium no excellent yes 31…40 high yes fair yes >40 medium no excellent no AVC-set on income AVC-set on Age AVC-set on Student Training Examples income Buy_Computer yes no high 2 2 medium 4 2 low 3 1 AVC-set on credit_rating

26 BOAT (Bootstrapped Optimistic Algorithm for Tree Construction)  Use a statistical technique called bootstrapping to create several smaller samples (subsets), each fits in memory  Each subset is used to create a tree, resulting in several trees  These trees are examined and used to construct a new tree T’  It turns out that T’ is very close to the tree that would be generated using the whole data set together  Adv: requires only two scans of DB, an incremental alg.

September 24, 2023 Data Mining: Concepts and Techniques 27 Presentation of Classification Results

September 24, 2023 Data Mining: Concepts and Techniques 28 SGI/MineSet 3.0

Data Mining: Concepts and Techniques 29 Interactive Visual Mining by Perception-Based Classification (PBC)

31 Bayesian Classification: Why?  A statistical classifier: performs probabilistic prediction, i.e., predicts class membership probabilities  Foundation: Based on Bayes’ Theorem.  Performance: A simple Bayesian classifier, naïve Bayesian classifier, has comparable performance with decision tree and selected neural network classifiers  Incremental: Each training example can incrementally increase/decrease the probability that a hypothesis is correct — prior knowledge can be combined with observed data  Standard: Even when Bayesian methods are computationally intractable, they can provide a standard of optimal decision making against which other methods can be measured

32 Bayes’ Theorem: Basics  Total probability Theorem:  Bayes’ Theorem:  Let X be a data sample (“evidence”): class label is unknown  Let H be a hypothesis that X belongs to class C  Classification is to determine P(H|X), (i.e., posteriori probability): the probability that the hypothesis holds given the observed data sample X  P(H) (prior probability): the initial probability  E.g., X will buy computer, regardless of age, income, …  P(X): probability that sample data is observed  P(X|H) (likelihood): the probability of observing the sample X, given that the hypothesis holds  E.g., Given that X will buy computer, the prob. that X is 31..40, medium income ) ( ) 1 | ( ) ( i A P M i i A B P B P    ) ( / ) ( ) | ( ) ( ) ( ) | ( ) | ( X X X X X P H P H P P H P H P H P   

33 Prediction Based on Bayes’ Theorem  Given training data X, posteriori probability of a hypothesis H, P(H|X), follows the Bayes’ theorem  Informally, this can be viewed as posteriori = likelihood x prior/evidence  Predicts X belongs to Ci iff the probability P(Ci|X) is the highest among all the P(Ck|X) for all the k classes  Practical difficulty: It requires initial knowledge of many probabilities, involving significant computational cost ) ( / ) ( ) | ( ) ( ) ( ) | ( ) | ( X X X X X P H P H P P H P H P H P   

34 Classification Is to Derive the Maximum Posteriori  Let D be a training set of tuples and their associated class labels, and each tuple is represented by an n-D attribute vector X = (x1, x2, …, xn)  Suppose there are m classes C1, C2, …, Cm.  Classification is to derive the maximum posteriori, i.e., the maximal P(Ci|X)  This can be derived from Bayes’ theorem  Since P(X) is constant for all classes, only needs to be maximized ) ( ) ( ) | ( ) | ( X X X P i C P i C P i C P  ) ( ) | ( ) | ( i C P i C P i C P X X 

35 Naïve Bayes Classifier  A simplified assumption: attributes are conditionally independent (i.e., no dependence relation between attributes):  This greatly reduces the computation cost: Only counts the class distribution  If Ak is categorical, P(xk|Ci) is the # of tuples in Ci having value xk for Ak divided by |Ci, D| (# of tuples of Ci in D)  If Ak is continous-valued, P(xk|Ci) is usually computed based on Gaussian distribution with a mean μ and standard deviation σ and P(xk|Ci) is ) | ( ... ) | ( ) | ( 1 ) | ( ) | ( 2 1 Ci x P Ci x P Ci x P n k Ci x P Ci P n k        X 2 2 2 ) ( 2 1 ) , , (          x e x g ) , , ( ) | ( i i C C k x g Ci P    X

36 Naïve Bayes Classifier: Training Dataset Class: C1:buys_computer = ‘yes’ C2:buys_computer = ‘no’ Data to be classified: X = (age <=30, Income = medium, Student = yes Credit_rating = Fair) age income student credit_rating buys_compu <=30 high no fair no <=30 high no excellent no 31…40 high no fair yes >40 medium no fair yes >40 low yes fair yes >40 low yes excellent no 31…40 low yes excellent yes <=30 medium no fair no <=30 low yes fair yes >40 medium yes fair yes <=30 medium yes excellent yes 31…40 medium no excellent yes 31…40 high yes fair yes >40 medium no excellent no

37 Naïve Bayes Classifier: An Example  P(Ci): P(buys_computer = “yes”) = 9/14 = 0.643 P(buys_computer = “no”) = 5/14= 0.357  Compute P(X|Ci) for each class P(age = “<=30” | buys_computer = “yes”) = 2/9 = 0.222 P(age = “<= 30” | buys_computer = “no”) = 3/5 = 0.6 P(income = “medium” | buys_computer = “yes”) = 4/9 = 0.444 P(income = “medium” | buys_computer = “no”) = 2/5 = 0.4 P(student = “yes” | buys_computer = “yes) = 6/9 = 0.667 P(student = “yes” | buys_computer = “no”) = 1/5 = 0.2 P(credit_rating = “fair” | buys_computer = “yes”) = 6/9 = 0.667 P(credit_rating = “fair” | buys_computer = “no”) = 2/5 = 0.4  X = (age <= 30 , income = medium, student = yes, credit_rating = fair) P(X|Ci) : P(X|buys_computer = “yes”) = 0.222 x 0.444 x 0.667 x 0.667 = 0.044 P(X|buys_computer = “no”) = 0.6 x 0.4 x 0.2 x 0.4 = 0.019 P(X|Ci)*P(Ci) : P(X|buys_computer = “yes”) * P(buys_computer = “yes”) = 0.028 P(X|buys_computer = “no”) * P(buys_computer = “no”) = 0.007 Therefore, X belongs to class (“buys_computer = yes”) age income student credit_rating buys_comp <=30 high no fair no <=30 high no excellent no 31…40 high no fair yes >40 medium no fair yes >40 low yes fair yes >40 low yes excellent no 31…40 low yes excellent yes <=30 medium no fair no <=30 low yes fair yes >40 medium yes fair yes <=30 medium yes excellent yes 31…40 medium no excellent yes 31…40 high yes fair yes >40 medium no excellent no

38 Avoiding the Zero-Probability Problem  Naïve Bayesian prediction requires each conditional prob. be non-zero. Otherwise, the predicted prob. will be zero  Ex. Suppose a dataset with 1000 tuples, income=low (0), income= medium (990), and income = high (10)  Use Laplacian correction (or Laplacian estimator)  Adding 1 to each case Prob(income = low) = 1/1003 Prob(income = medium) = 991/1003 Prob(income = high) = 11/1003  The “corrected” prob. estimates are close to their “uncorrected” counterparts    n k Ci xk P Ci X P 1 ) | ( ) | (

39 Naïve Bayes Classifier: Comments  Advantages  Easy to implement  Good results obtained in most of the cases  Disadvantages  Assumption: class conditional independence, therefore loss of accuracy  Practically, dependencies exist among variables  E.g., hospitals: patients: Profile: age, family history, etc. Symptoms: fever, cough etc., Disease: lung cancer, diabetes, etc.  Dependencies among these cannot be modeled by Naïve Bayes Classifier  How to deal with these dependencies? Bayesian Belief Networks (Chapter 9)

41 Using IF-THEN Rules for Classification  Represent the knowledge in the form of IF-THEN rules R: IF age = youth AND student = yes THEN buys_computer = yes  Rule antecedent/precondition vs. rule consequent  Assessment of a rule: coverage and accuracy  ncovers = # of tuples covered by R  ncorrect = # of tuples correctly classified by R coverage(R) = ncovers /|D| /* D: training data set */ accuracy(R) = ncorrect / ncovers  If more than one rule are triggered, need conflict resolution  Size ordering: assign the highest priority to the triggering rules that has the “toughest” requirement (i.e., with the most attribute tests)  Class-based ordering: decreasing order of prevalence or misclassification cost per class  Rule-based ordering (decision list): rules are organized into one long priority list, according to some measure of rule quality or by experts

42 age? student? credit rating? <=30 >40 no yes yes yes 31..40 fair excellent yes no  Example: Rule extraction from our buys_computer decision-tree IF age = young AND student = no THEN buys_computer = no IF age = young AND student = yes THEN buys_computer = yes IF age = mid-age THEN buys_computer = yes IF age = old AND credit_rating = excellent THEN buys_computer = no IF age = old AND credit_rating = fair THEN buys_computer = yes Rule Extraction from a Decision Tree  Rules are easier to understand than large trees  One rule is created for each path from the root to a leaf  Each attribute-value pair along a path forms a conjunction: the leaf holds the class prediction  Rules are mutually exclusive and exhaustive

43 Rule Induction: Sequential Covering Method  Sequential covering algorithm: Extracts rules directly from training data  Typical sequential covering algorithms: FOIL, AQ, CN2, RIPPER  Rules are learned sequentially, each for a given class Ci will cover many tuples of Ci but none (or few) of the tuples of other classes  Steps:  Rules are learned one at a time  Each time a rule is learned, the tuples covered by the rules are removed  Repeat the process on the remaining tuples until termination condition, e.g., when no more training examples or when the quality of a rule returned is below a user-specified threshold  Comp. w. decision-tree induction: learning a set of rules simultaneously

44 Sequential Covering Algorithm while (enough target tuples left) generate a rule remove positive target tuples satisfying this rule Examples covered by Rule 3 Examples covered by Rule 2 Examples covered by Rule 1 Positive examples

45 Rule Generation  To generate a rule while(true) find the best predicate p if foil-gain(p) > threshold then add p to current rule else break Positive examples Negative examples A3=1 A3=1&&A1=2 A3=1&&A1=2 &&A8=5

46 How to Learn-One-Rule?  Start with the most general rule possible: condition = empty  Adding new attributes by adopting a greedy depth-first strategy  Picks the one that most improves the rule quality  Rule-Quality measures: consider both coverage and accuracy  Foil-gain (in FOIL & RIPPER): assesses info_gain by extending condition  favors rules that have high accuracy and cover many positive tuples  Rule pruning based on an independent set of test tuples Pos/neg are # of positive/negative tuples covered by R. If FOIL_Prune is higher for the pruned version of R, prune R ) log ' ' ' (log ' _ 2 2 neg pos pos neg pos pos pos Gain FOIL      neg pos neg pos R Prune FOIL    ) ( _

Model Evaluation and Selection  Evaluation metrics: How can we measure accuracy? Other metrics to consider?  Use validation test set of class-labeled tuples instead of training set when assessing accuracy  Methods for estimating a classifier’s accuracy:  Holdout method, random subsampling  Cross-validation  Bootstrap  Comparing classifiers:  Confidence intervals  Cost-benefit analysis and ROC Curves 48

Classifier Evaluation Metrics: Confusion Matrix Actual classPredicted class buy_computer = yes buy_computer = no Total buy_computer = yes 6954 46 7000 buy_computer = no 412 2588 3000 Total 7366 2634 10000  Given m classes, an entry, CMi,j in a confusion matrix indicates # of tuples in class i that were labeled by the classifier as class j  May have extra rows/columns to provide totals Confusion Matrix: Actual classPredicted class C1 ¬ C1 C1 True Positives (TP) False Negatives (FN) ¬ C1 False Positives (FP) True Negatives (TN) Example of Confusion Matrix: 49

Accuracy, Error Rate, Sensitivity and Specificity  Classifier Accuracy, or recognition rate: percentage of test set tuples that are correctly classified Accuracy = (TP + TN)/All  Error rate: 1 – accuracy, or Error rate = (FP + FN)/All  Class Imbalance Problem:  One class may be rare, e.g. fraud, or HIV-positive  Significant majority of the negative class and minority of the positive class  Sensitivity: True Positive recognition rate  Sensitivity = TP/P  Specificity: True Negative recognition rate  Specificity = TN/N AP C ¬C C TP FN P ¬C FP TN N P’ N’ All 50

Precision and Recall, and F- measures  Precision: exactness – what % of tuples that the classifier labeled as positive are actually positive  Recall: completeness – what % of positive tuples did the classifier label as positive?  Perfect score is 1.0  Inverse relationship between precision & recall  F measure (F1 or F-score): harmonic mean of precision and recall,  Fß: weighted measure of precision and recall  assigns ß times as much weight to recall as to precision 51

Classifier Evaluation Metrics: Example 52  Precision = 90/230 = 39.13% Recall = 90/300 = 30.00% Actual ClassPredicted class cancer = yes cancer = no Total Recognition(%) cancer = yes 90 210 300 30.00 (sensitivity cancer = no 140 9560 9700 98.56 (specificity) Total 230 9770 10000 96.40 (accuracy)

Holdout & Cross-Validation Methods  Holdout method  Given data is randomly partitioned into two independent sets  Training set (e.g., 2/3) for model construction  Test set (e.g., 1/3) for accuracy estimation  Random sampling: a variation of holdout  Repeat holdout k times, accuracy = avg. of the accuracies obtained  Cross-validation (k-fold, where k = 10 is most popular)  Randomly partition the data into k mutually exclusive subsets, each approximately equal size  At i-th iteration, use Di as test set and others as training set  Leave-one-out: k folds where k = # of tuples, for small sized data  *Stratified cross-validation*: folds are stratified so that class dist. in each fold is approx. the same as that in the initial data 53

Evaluating Classifier Accuracy: Bootstrap  Bootstrap  Works well with small data sets  Samples the given training tuples uniformly with replacement  i.e., each time a tuple is selected, it is equally likely to be selected again and re-added to the training set  Several bootstrap methods, and a common one is .632 boostrap  A data set with d tuples is sampled d times, with replacement, resulting in a training set of d samples. The data tuples that did not make it into the training set end up forming the test set. About 63.2% of the original data end up in the bootstrap, and the remaining 36.8% form the test set (since (1 – 1/d)d ≈ e-1 = 0.368)  Repeat the sampling procedure k times, overall accuracy of the model: 54

Estimating Confidence Intervals: Classifier Models M1 vs. M2  Suppose we have 2 classifiers, M1 and M2, which one is better?  Use 10-fold cross-validation to obtain and  These mean error rates are just estimates of error on the true population of future data cases  What if the difference between the 2 error rates is just attributed to chance?  Use a test of statistical significance  Obtain confidence limits for our error estimates 55

Estimating Confidence Intervals: Null Hypothesis  Perform 10-fold cross-validation  Assume samples follow a t distribution with k–1 degrees of freedom (here, k=10)  Use t-test (or Student’s t-test)  Null Hypothesis: M1 & M2 are the same  If we can reject null hypothesis, then  we conclude that the difference between M1 & M2 is statistically significant  Chose model with lower error rate 56

Estimating Confidence Intervals: t-test  If only 1 test set available: pairwise comparison  For ith round of 10-fold cross-validation, the same cross partitioning is used to obtain err(M1)i and err(M2)i  Average over 10 rounds to get  t-test computes t-statistic with k-1 degrees of freedom:  If two test sets available: use non-paired t-test where and where where k1 & k2 are # of cross-validation samples used for M1 & M2, resp. 57

Estimating Confidence Intervals: Table for t-distribution  Symmetric  Significance level, e.g., sig = 0.05 or 5% means M1 & M2 are significantly different for 95% of population  Confidence limit, z = sig/2 58

Estimating Confidence Intervals: Statistical Significance  Are M1 & M2 significantly different?  Compute t. Select significance level (e.g. sig = 5%)  Consult table for t-distribution: Find t value corresponding to k-1 degrees of freedom (here, 9)  t-distribution is symmetric: typically upper % points of distribution shown → look up value for confidence limit z=sig/2 (here, 0.025)  If t > z or t < -z, then t value lies in rejection region:  Reject null hypothesis that mean error rates of M1 & M2 are same  Conclude: statistically significant difference between M1 & M2  Otherwise, conclude that any difference is chance 59

Model Selection: ROC Curves  ROC (Receiver Operating Characteristics) curves: for visual comparison of classification models  Originated from signal detection theory  Shows the trade-off between the true positive rate and the false positive rate  The area under the ROC curve is a measure of the accuracy of the model  Rank the test tuples in decreasing order: the one that is most likely to belong to the positive class appears at the top of the list  The closer to the diagonal line (i.e., the closer the area is to 0.5), the less accurate is the model  Vertical axis represents the true positive rate  Horizontal axis rep. the false positive rate  The plot also shows a diagonal line  A model with perfect accuracy will have an area of 1.0 60

Issues Affecting Model Selection  Accuracy  classifier accuracy: predicting class label  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 61

Ensemble Methods: Increasing the Accuracy  Ensemble methods  Use a combination of models to increase accuracy  Combine a series of k learned models, M1, M2, …, Mk, with the aim of creating an improved model M*  Popular ensemble methods  Bagging: averaging the prediction over a collection of classifiers  Boosting: weighted vote with a collection of classifiers  Ensemble: combining a set of heterogeneous classifiers 63

Bagging: Boostrap Aggregation  Analogy: Diagnosis based on multiple doctors’ majority vote  Training  Given a set D of d tuples, at each iteration i, a training set Di of d tuples is sampled with replacement from D (i.e., bootstrap)  A classifier model Mi is learned for each training set Di  Classification: classify an unknown sample X  Each classifier Mi returns its class prediction  The bagged classifier M* counts the votes and assigns the class with the most votes to X  Prediction: can be applied to the prediction of continuous values by taking the average value of each prediction for a given test tuple  Accuracy  Often significantly better than a single classifier derived from D  For noise data: not considerably worse, more robust  Proved improved accuracy in prediction 64

Boosting  Analogy: Consult several doctors, based on a combination of weighted diagnoses—weight assigned based on the previous diagnosis accuracy  How boosting works?  Weights are assigned to each training tuple  A series of k classifiers is iteratively learned  After a classifier Mi is learned, the weights are updated to allow the subsequent classifier, Mi+1, to pay more attention to the training tuples that were misclassified by Mi  The final M* combines the votes of each individual classifier, where the weight of each classifier's vote is a function of its accuracy  Boosting algorithm can be extended for numeric prediction  Comparing with bagging: Boosting tends to have greater accuracy, but it also risks overfitting the model to misclassified data 65

66 Adaboost (Freund and Schapire, 1997)  Given a set of d class-labeled tuples, (X1, y1), …, (Xd, yd)  Initially, all the weights of tuples are set the same (1/d)  Generate k classifiers in k rounds. At round i,  Tuples from D are sampled (with replacement) to form a training set Di of the same size  Each tuple’s chance of being selected is based on its weight  A classification model Mi is derived from Di  Its error rate is calculated using Di as a test set  If a tuple is misclassified, its weight is increased, o.w. it is decreased  Error rate: err(Xj) is the misclassification error of tuple Xj. Classifier Mi error rate is the sum of the weights of the misclassified tuples:  The weight of classifier Mi’s vote is ) ( ) ( 1 log i i M error M error     d j j i err w M error ) ( ) ( j X

Random Forest (Breiman 2001)  Random Forest:  Each classifier in the ensemble is a decision tree classifier and is generated using a random selection of attributes at each node to determine the split  During classification, each tree votes and the most popular class is returned  Two Methods to construct Random Forest:  Forest-RI (random input selection): Randomly select, at each node, F attributes as candidates for the split at the node. The CART methodology is used to grow the trees to maximum size  Forest-RC (random linear combinations): Creates new attributes (or features) that are a linear combination of the existing attributes (reduces the correlation between individual classifiers)  Comparable in accuracy to Adaboost, but more robust to errors and outliers  Insensitive to the number of attributes selected for consideration at each split, and faster than bagging or boosting 67

Classification of Class-Imbalanced Data Sets  Class-imbalance problem: Rare positive example but numerous negative ones, e.g., medical diagnosis, fraud, oil-spill, fault, etc.  Traditional methods assume a balanced distribution of classes and equal error costs: not suitable for class-imbalanced data  Typical methods for imbalance data in 2-class classification:  Oversampling: re-sampling of data from positive class  Under-sampling: randomly eliminate tuples from negative class  Threshold-moving: moves the decision threshold, t, so that the rare class tuples are easier to classify, and hence, less chance of costly false negative errors  Ensemble techniques: Ensemble multiple classifiers introduced above  Still difficult for class imbalance problem on multiclass tasks 68

Summary (I)  Classification is a form of data analysis that extracts models describing important data classes.  Effective and scalable methods have been developed for decision tree induction, Naive Bayesian classification, rule-based classification, and many other classification methods.  Evaluation metrics include: accuracy, sensitivity, specificity, precision, recall, F measure, and Fß measure.  Stratified k-fold cross-validation is recommended for accuracy estimation. Bagging and boosting can be used to increase overall accuracy by learning and combining a series of individual models. 70

Summary (II)  Significance tests and ROC curves are useful for model selection.  There have been numerous comparisons of the different classification methods; the matter remains a research topic  No single method has been found to be superior over all others for all data sets  Issues such as accuracy, training time, robustness, scalability, and interpretability must be considered and can involve trade- offs, further complicating the quest for an overall superior method 71

References (1)  C. Apte and S. Weiss. Data mining with decision trees and decision rules. Future Generation Computer Systems, 13, 1997  C. M. Bishop, Neural Networks for Pattern Recognition. Oxford University Press, 1995  L. Breiman, J. Friedman, R. Olshen, and C. Stone. Classification and Regression Trees. Wadsworth International Group, 1984  C. J. C. Burges. A Tutorial on Support Vector Machines for Pattern Recognition. Data Mining and Knowledge Discovery, 2(2): 121-168, 1998  P. K. Chan and S. J. Stolfo. Learning arbiter and combiner trees from partitioned data for scaling machine learning. KDD'95  H. Cheng, X. Yan, J. Han, and C.-W. Hsu, Discriminative Frequent Pattern Analysis for Effective Classification, ICDE'07  H. Cheng, X. Yan, J. Han, and P. S. Yu, Direct Discriminative Pattern Mining for Effective Classification, ICDE'08  W. Cohen. Fast effective rule induction. ICML'95  G. Cong, K.-L. Tan, A. K. H. Tung, and X. Xu. Mining top-k covering rule groups for gene expression data. SIGMOD'05 72

References (2)  A. J. Dobson. An Introduction to Generalized Linear Models. Chapman & Hall, 1990.  G. Dong and J. Li. Efficient mining of emerging patterns: Discovering trends and differences. KDD'99.  R. O. Duda, P. E. Hart, and D. G. Stork. Pattern Classification, 2ed. John Wiley, 2001  U. M. Fayyad. Branching on attribute values in decision tree generation. AAAI’94.  Y. Freund and R. E. Schapire. A decision-theoretic generalization of on-line learning and an application to boosting. J. Computer and System Sciences, 1997.  J. Gehrke, R. Ramakrishnan, and V. Ganti. Rainforest: A framework for fast decision tree construction of large datasets. VLDB’98.  J. Gehrke, V. Gant, R. Ramakrishnan, and W.-Y. Loh, BOAT -- Optimistic Decision Tree Construction. SIGMOD'99.  T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer-Verlag, 2001.  D. Heckerman, D. Geiger, and D. M. Chickering. Learning Bayesian networks: The combination of knowledge and statistical data. Machine Learning, 1995.  W. Li, J. Han, and J. Pei, CMAR: Accurate and Efficient Classification Based on Multiple Class-Association Rules, ICDM'01. 73

References (3)  T.-S. Lim, W.-Y. Loh, and Y.-S. Shih. A comparison of prediction accuracy, complexity, and training time of thirty-three old and new classification algorithms. Machine Learning, 2000.  J. Magidson. The Chaid approach to segmentation modeling: Chi-squared automatic interaction detection. In R. P. Bagozzi, editor, Advanced Methods of Marketing Research, Blackwell Business, 1994.  M. Mehta, R. Agrawal, and J. Rissanen. SLIQ : A fast scalable classifier for data mining. EDBT'96.  T. M. Mitchell. Machine Learning. McGraw Hill, 1997.  S. K. Murthy, Automatic Construction of Decision Trees from Data: A Multi- Disciplinary Survey, Data Mining and Knowledge Discovery 2(4): 345-389, 1998  J. R. Quinlan. Induction of decision trees. Machine Learning, 1:81-106, 1986.  J. R. Quinlan and R. M. Cameron-Jones. FOIL: A midterm report. ECML’93.  J. R. Quinlan. C4.5: Programs for Machine Learning. Morgan Kaufmann, 1993.  J. R. Quinlan. Bagging, boosting, and c4.5. AAAI'96. 74

References (4)  R. Rastogi and K. Shim. Public: A decision tree classifier that integrates building and pruning. VLDB’98.  J. Shafer, R. Agrawal, and M. Mehta. SPRINT : A scalable parallel classifier for data mining. VLDB’96.  J. W. Shavlik and T. G. Dietterich. Readings in Machine Learning. Morgan Kaufmann, 1990.  P. Tan, M. Steinbach, and V. Kumar. Introduction to Data Mining. Addison Wesley, 2005.  S. M. Weiss and C. A. Kulikowski. Computer Systems that Learn: Classification and Prediction Methods from Statistics, Neural Nets, Machine Learning, and Expert Systems. Morgan Kaufman, 1991.  S. M. Weiss and N. Indurkhya. Predictive Data Mining. Morgan Kaufmann, 1997.  I. H. Witten and E. Frank. Data Mining: Practical Machine Learning Tools and Techniques, 2ed. Morgan Kaufmann, 2005.  X. Yin and J. Han. CPAR: Classification based on predictive association rules. SDM'03  H. Yu, J. Yang, and J. Han. Classifying large data sets using SVM with hierarchical clusters. KDD'03. 75

CS412 Midterm Exam Statistics  Opinion Question Answering:  Like the style: 70.83%, dislike: 29.16%  Exam is hard: 55.75%, easy: 0.6%, just right: 43.63%  Time: plenty:3.03%, enough: 36.96%, not: 60%  Score distribution: # of students (Total: 180)  >=90: 24  80-89: 54  70-79: 46  Final grading are based on overall score accumulation and relative class distributions 77  60-69: 37  50-59: 15  40-49: 2  <40: 2

78 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

79 Predictor Error Measures  Measure predictor accuracy: measure how far off the predicted value is from the actual known value  Loss function: measures the error betw. yi and the predicted value yi’  Absolute error: | yi – yi’|  Squared error: (yi – yi’)2  Test error (generalization error): the average loss over the test set  Mean absolute error: Mean squared error:  Relative absolute error: Relative squared error: The mean squared-error exaggerates the presence of outliers Popularly use (square) root mean-square error, similarly, root relative squared error d y y d i i i    1 | ' | d y y d i i i    1 2 ) ' (       d i i d i i i y y y y 1 1 | | | ' |       d i i d i i i y y y y 1 2 1 2 ) ( ) ' (

80 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

81 Data Cube-Based Decision-Tree Induction  Integration of generalization with decision-tree induction (Kamber et al.’97)  Classification at primitive concept levels  E.g., precise temperature, humidity, outlook, etc.  Low-level concepts, scattered classes, bushy classification- trees  Semantic interpretation problems  Cube-based multi-level classification  Relevance analysis at multi-levels  Information-gain analysis with dimension + level

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Chapter 8. Classification Basic Concepts.ppt