Agenda
 Classification: Basic Concepts
 Decision Tree Induction
 Bayes Classification Methods
 RuleBased Classification
 Model Evaluation and Selection
 Techniques to Improve Classification Accuracy: Ensemble Methods
 Summary
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
 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 continuousvalued 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
Classification—A TwoStep 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
Process (1): Model Construction
Process (2): Using the Model in Prediction
Decision Tree Induction: An Example
Algorithm for Decision Tree Induction
 Basic algorithm (a greedy algorithm)
 Tree is constructed in a topdown recursive divideandconquer manner
 At start, all the training examples are at the root
 Attributes are categorical (if continuousvalued, 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
 Entropy (Information Theory)
 A measure of uncertainity associated with a random variable
 Calculation: for a discrete random variable Y taking m distinct values {y1,...,ym},
\[H(Y)=\sum_{i=1}^{m}p_{i}log(p_{i}), p_{i}=P(Y=y_{i})\]
 Interpretation:
 Higher entropy=>higher uncertainty
 Lower entropy=>lower uncertainty
 Higher entropy=>higher uncertainty
 Conditional entropy
\[H(YX)=\sum_{x}p(x)H(YX=x)\]
Attribute Selection Measure: Information Gain (ID3/C4.5)
 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
\[ \frac{ C_{i,D}} {D}\]
 Expected information (entropy) needed to classify a tuple in D:
\[Info(D)=\sum_{i=1}^{m} p_{i}log_{2}(p_{i})\]
 Information needed (after using A to split D into v partitions) to classify D:
\[Info_{A}(D)=\sum_{j=1}^{v} \frac{D_{j}}{D}\times Info (D_{j})\]
 Information gained by branching on attribute A
\[Gain(A)=Info(D)Info_{A}(D)\]
Attribute Selection: Information Gain
Computing InformationGain for ContinuousValued Attributes
 Let attribute A be a continuousvalued 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 splitpoint for A
 Split:
 D1 is the set of tuples in D satisfying A ≤ splitpoint, and D2 is the set of tuples in D satisfying A > splitpoint
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)
\[SplitInfo_{A}(D)=\sum_{j=1}^{v} \frac{D_{j}}{D}\times log_{2}(\frac{D_{j}}{D})\]
\[GainRatio(A) = \frac{Gain(A)}{SplitInfo(A)}\]
 Ex.
 gain_ratio(income) = 0.029/1.557 = 0.019
 The attribute with the maximum gain ratio is selected as the splitting attribute
Gini Index (CART, IBM IntelligentMiner)
 If a data set D contains examples from n classes, gini index, gini(D) is defined as
\[gini(D)=1\sum_{j=1}^{n}p^{2}j\]
 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
\[gini_{A}(D)=\frac{D_{1}}{D}gini(D_{1})+\frac{D_{2}}{D} gini(D_{1})\]
 Reduction in Impurity:
\[\Delta gini(A)=gini(D)gini_{A}(D)\]
 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)
Computation of Gini Index
 Ex. D has 9 tuples in buys_computer = “yes” and 5 in “no”
\[gini(D)=1\left ( \frac{9}{14} \right )^{2}\left ( \frac{5}{14} \right )^{2}=0.459\]
 Suppose the attribute income partitions D into 10 in D1: {low, medium} and 4 in D2
\[gini_{income\epsilon \left \{ low,medium \right \}}(D)=\left ( \frac{10}{14} \right )Gini(D_{1})+\left ( \frac{4}{14} \right )Gini(D_{2})\]
\[\frac{10}{14}\left (1\left ( \frac{7}{10} \right )^{2}\left ( \frac{3}{10} \right )^{2} \right )+\frac{4}{14}\left (1\left ( \frac{2}{4} \right )^{2}\left ( \frac{2}{4} \right )^{2} \right )\]
\[=0.443=gini_{income\epsilon \left \{ high \right \}}(D)\]
 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 continuousvalued
 May need other tools, e.g., clustering, to get the possible split values
 Can be modified for categorical attributes
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 equalsized partitions and purity in both partitions
Other Attribute Selection Measures
 CHAID: a popular decision tree algorithm, measure based on χ2 test for independence
 CSEP: performs better than info. gain and gini index in certain cases
 Gstatistic: has a close approximation to χ^2 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
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”
Enhancements to Basic Decision Tree Induction
 Allow for continuousvalued attributes
 Dynamically define new discretevalued 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 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 AVClist (attribute, value, class label)
Scalability Framework for RainForest
 Separates the scalability aspects from the criteria that determine the quality of the tree
 Builds an AVClist: AVC (Attribute, Value, Class_label)
 AVCset (of an attribute X )
 Projection of training dataset onto the attribute X and class label where counts of individual class label are aggregated
 AVCgroup (of a node n )
 Set of AVCsets of all predictor attributes at the node n
Rainforest: Training Set and Its AVC Sets
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.
Presentation of Classification Results
Visualization of a Decision Tree in SGI/MineSet 3.0
Interactive Visual Mining by PerceptionBased Classification (PBC)
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
Bayes’ Theorem: Basics
 Total probability Theorem:
\[P(B)=\sum_{i=1}^{M}P(BA_{i})P(A_{i})\]
 Bayes’ Theorem:
\[P(HX)=\frac{P(XH)P(H)}{P(X)}=P(XH)\times P(H)/P(X)\]
 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(HX), (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(XH) (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
Prediction Based on Bayes’ Theorem
 Given training data X, posteriori probability of a hypothesis H, P(HX), follows the Bayes’ theorem
\[P(HX)=\frac{P(XH)P(H)}{P(X)}=P(XH)\times P(H)/P(X)\]
 Informally, this can be viewed as
 posteriori = likelihood x prior/evidence
 Predicts X belongs to Ci iff the probability P(CiX) is the highest among all the P(CkX) for all the k classes
 Practical difficulty: It requires initial knowledge of many probabilities, involving significant computational cost
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 nD 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(CiX)
 This can be derived from Bayes’ theorem
\[P(C_{i}X)=\frac{P(XC_{i})P(C_{i})}{P(X)}\]
 Since P(X) is constant for all classes, only
\[P(C_{i}X)=P(XC_{i})P(C_{i})\]
needs to be maximized
Naïve Bayes Classifier
 A simplified assumption: attributes are conditionally independent (i.e., no dependence relation between attributes):
\[P(XC_{i})=\prod_{k=1}^{n}P(x_{k}C_{i})=P(x_{1}C_{i})\times P(x_{2}C_{i})\times ... \times P(x_{n}C_{i})\]
 This greatly reduces the computation cost: Only counts the class distribution
 If Ak is categorical, P(xkCi) is the # of tuples in Ci having value xk for Ak divided by Ci, D (# of tuples of Ci in D)
 If Ak is continousvalued, P(xkCi) is usually computed based on Gaussian distribution with a mean μ and standard deviation σ
\[g(x,\mu,\sigma)=\frac{1}{\sqrt{2\pi}\sigma}e^{\frac{(x\mu)^{2}}{2\sigma ^{2}}}\]
 and P(xkCi) is
\[P(XC_{i})=g(x_{k},\mu_{C_{i}},\sigma_{C_{i}})\]
Naïve Bayes Classifier: Training Dataset
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(XCi) 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(XCi) : P(Xbuys_computer = “yes”) = 0.222 x 0.444 x 0.667 x 0.667 = 0.044
P(Xbuys_computer = “no”) = 0.6 x 0.4 x 0.2 x 0.4 = 0.019
P(XCi)*P(Ci) : P(Xbuys_computer = “yes”) * P(buys_computer = “yes”) = 0.028
P(Xbuys_computer = “no”) * P(buys_computer = “no”) = 0.007
Therefore, X belongs to class (“buys_computer = yes”)
Avoiding the ZeroProbability Problem
 Naïve Bayesian prediction requires each conditional prob. be nonzero. Otherwise, the predicted prob. will be zero
\[P(XC_{i})=\prod_{k=1}^{n}P(x_{k}C_{i})\]
 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
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
Using IFTHEN Rules for Classification
 Represent the knowledge in the form of IFTHEN 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)
 Classbased ordering: decreasing order of prevalence or misclassification cost per class
 Rulebased ordering (decision list): rules are organized into one long priority list, according to some measure of rule quality or by experts
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 attributevalue pair along a path forms a conjunction: the leaf holds the class prediction
 Rules are mutually exclusive and exhaustive
 Example: Rule extraction from our buys_computer decisiontree
IF age = young AND student = no THEN buys_computer = no
IF age = young AND student = yes THEN buys_computer = yes
IF age = midage 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 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 userspecified threshold
 Comp. w. decisiontree induction: learning a set of rules simultaneously
Sequential Covering Algorithm
while (enough target tuples left)generate a rule
remove positive target tuples satisfying this rule
Rule Generation
 To generate a rule
while(true)
find the best predicate p
if foilgain(p) > threshold then add p to current rule
else break
How to LearnOneRule?
 Start with the most general rule possible: condition = empty
 Adding new attributes by adopting a greedy depthfirst strategy
 Picks the one that most improves the rule quality
 RuleQuality measures: consider both coverage and accuracy
 Foilgain (in FOIL & RIPPER): assesses info_gain by extending condition
\[FOILGain=pos{'} \times \left ( log_{2}\frac{pos'}{pos'+neg'}log_{2}\frac{pos}{pos+neg} \right )\]
 favors rules that have high accuracy and cover many positive tuples
 Rule pruning based on an independent set of test tuples
\[FOILPrune(R)=\frac{posneg}{pos+neg} \right )\]
 Pos/neg are # of positive/negative tuples covered by R.
 If FOIL_Prune is higher for the pruned version of R, prune R
Model Evaluation and Selection
 Evaluation metrics: How can we measure accuracy? Other metrics to consider?
 Use validation test set of classlabeled tuples instead of training set when assessing accuracy
 Methods for estimating a classifier’s accuracy:
 Holdout method, random subsampling
 Crossvalidation
 Bootstrap
 Comparing classifiers:
 Confidence intervals
 Costbenefit analysis and ROC Curves
Classifier Evaluation Metrics: Confusion Matrix
 Given m classes, an entry, CM i,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
Classifier Evaluation Metrics: Accuracy, Error Rate, Sensitivity and Specificity


Classifier Evaluation Metrics: Precision and Recall, and Fmeasures
 Precision: exactness – what % of tuples that the classifier labeled as positive are actually positive
\[precision=\frac{TP}{TP+FP}\]
 Recall: completeness – what % of positive tuples did the classifier label as positive?
\[recall=\frac{TP}{TP+FN}\]
 Perfect score is 1.0
 Inverse relationship between precision & recall
 F measure (F1 or Fscore): harmonic mean of precision and recall,
\[F=\frac{2\times precision \times recall}{precision+recall}\]
 Fß: weighted measure of precision and recall
 assigns ß times as much weight to recall as to precision
Classifier Evaluation Metrics: Example
Actual Class\Predicted 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 ) 
Precision = 90/230 = 39.13% Recall = 90/300 = 30.00%
Evaluating Classifier Accuracy: Holdout & CrossValidation 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
 Crossvalidation (kfold, where k = 10 is most popular)
 Randomly partition the data into k mutually exclusive subsets, each approximately equal size
 At ith iteration, use Di as test set and others as training set
 Leaveoneout: k folds where k = # of tuples, for small sized data
 *Stratified crossvalidation*: folds are stratified so that class dist. in each fold is approx. the same as that in the initial data
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 readded 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 ≈ e1 = 0.368)
 Repeat the sampling procedure k times, overall accuracy of the model:
\[Acc(M)=\frac{1}{k}\sum_{i=1}^{k}(0.632 \times Acc(M_{i})_{testset}+0.368 \times Acc(M_{i})_{trainset})\]
Estimating Confidence Intervals: Classifier Models M1 vs. M2
 Suppose we have 2 classifiers, M1 and M2, which one is better?
 Use 10fold crossvalidation to obtain err'(M1) and err'(M2)
 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
Estimating Confidence Intervals: Null Hypothesis
 Perform 10fold crossvalidation
 Assume samples follow a t distribution with k–1 degrees of freedom (here, k=10)
 Use ttest (or Student’s ttest)
 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
Estimating Confidence Intervals: ttest
 If only 1 test set available: pairwise comparison
 For ith round of 10fold crossvalidation, the same cross partitioning is used to obtain err(M1)i and err(M2)i
 Average over 10 rounds to get err'(M1) and err'(M2)
 ttest computes tstatistic with k1 degrees of freedom:
\[t=\frac{\bar{err}(M_{1})\bar{err}(M_{2})}{\sqrt{var(M_{1}M_{2})/k}}\]
\[var(M_{1}M_{2})=\frac{1}{k}\sum_{i=1}^{k}\left [err(M_{1})_{i}  err(M_{2})_{i} (\bar{err}(M_{1})\bar{err}(M_{2}))\right ]^{2}\]
 If two test sets available: use nonpaired ttest
\[var(M_{1}M_{2})=\sqrt{\frac{var(M_{1})}{k_{1}}+\frac{var(M_{2})}{k_{2}}}\]
where k1 & k2 are # of crossvalidation samples used for M1 & M2, resp.
Estimating Confidence Intervals: Table for tdistribution

Estimating Confidence Intervals: Statistical Significance
 Are M1 & M2 significantly different?
 Compute t. Select significance level (e.g. sig = 5%)
 Consult table for tdistribution: Find t value corresponding to k1 degrees of freedom (here, 9)
 tdistribution 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
Model Selection: ROC Curves


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 diskresident 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
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 diskresident 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
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:
\[\frac{\sum_{i=1}^{d}y_{i}y_{i}^{'}}{d}\]
Mean squared error:
\[\frac{\sum_{i=1}^{d}(y_{i}y_{i}^{'})^{2}}{d}\]
Relative absolute error:
\[\frac{\sum_{i=1}^{d}y_{i}y_{i}^{'}}{\sum_{i=1}^{d}y_{i}\bar{y}}\]
Relative squared error:
\[\frac{\sum_{i=1}^{d}(y_{i}y_{i}^{'})^{2}}{\sum_{i=1}^{d}(y_{i}\bar{y})^{2}}\]
The mean squarederror exaggerates the presence of outliers
Popularly use (square) root meansquare error, similarly, root relative squared error
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 AVClist (attribute, value, class label)
 BOAT (PODS’99 — Gehrke, Ganti, Ramakrishnan & Loh)
 Uses bootstrapping to create several small samples
Data CubeBased DecisionTree Induction
 Integration of generalization with decisiontree induction (Kamber et al.’97)
 Classification at primitive concept levels
 E.g., precise temperature, humidity, outlook, etc.
 Lowlevel concepts, scattered classes, bushy classificationtrees
 Semantic interpretation problems
 Cubebased multilevel classification
 Relevance analysis at multilevels
 Informationgain analysis with dimension + level
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
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
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
Adaboost (Freund and Schapire, 1997)
 Given a set of d classlabeled 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:
\[error(M_{i})=\sum_{j}^{d}w_{j}\times err (X_{j})\]
 The weight of classifier Mi’s vote is
\[log \frac{1error(M_{i})}{error(M_{i})}\]
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:
 ForestRI (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
 ForestRC (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
Classification of ClassImbalanced Data Sets
 Classimbalance problem: Rare positive example but numerous negative ones, e.g., medical diagnosis, fraud, oilspill, fault, etc.
 Traditional methods assume a balanced distribution of classes and equal error costs: not suitable for classimbalanced data
 Typical methods for imbalance data in 2class classification:
 Oversampling: resampling of data from positive class
 Undersampling: randomly eliminate tuples from negative class
 Thresholdmoving: 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
Summary
 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, rulebased classification, and many other classification methods.
 Evaluation metrics include: accuracy, sensitivity, specificity, precision, recall, F measure, and Fß measure.
 Stratified kfold crossvalidation is recommended for accuracy estimation. Bagging and boosting can be used to increase overall accuracy by learning and combining a series of individual models.
 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 tradeoffs, further complicating the quest for an overall superior method
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