第4课数据分类和预测.ppt

*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,第4课 数据分类和预测,徐从富，,副教授,浙江大学人工智能研究所,浙江大学本科生数据挖掘导论课件,内容提纲,What is classification?What is prediction?,Issues regarding classification and prediction,Classification by decision tree induction,Bayesian Classification,Prediction,Summary,Reference,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,Prediction,models continuous-valued functions,i.e.,predicts unknown or missing values,Typical applications,Credit approval,Target marketing,Medical diagnosis,Fraud detection,Classification vs.Prediction,ClassificationA 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,Classification Process(1):Model Construction,Training,Data,Classification,Algorithms,IF rank=professor,OR years 6,THEN tenured=yes,Classifier,(Model),Issues Regarding Classification and Prediction(1):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 regarding classification and prediction(2):Evaluating classification methods,Accuracy:classifier accuracy and predictor accuracy,Speed and scalability,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,Decision Tree Induction:Training Dataset,This follows an example of Quinlans ID3(Playing Tennis),Output:A Decision Tree for“,buys_computer,”,age?,overcast,student?,credit rating?,no,yes,fair,excellent,40,no,no,yes,yes,yes,30.40,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,Attribute Selection Measure:Information Gain(ID3/C4.5),Select the attribute with the highest information gain,S,contains,s,i,tuples,of class,C,i,for,i,=,1,m,information,measures info required to classify any arbitrary,tuple,entropy,of attribute,A,with values,a,1,a,2,a,v,information gained,by branching on attribute,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,:,means“age split-point,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,Each attribute-value pair along a path forms a conjunction,The leaf node holds the class prediction,Rules are easier for humans to understand,Example,IF,age,=“=30”AND,student,=“,no,”,THEN,buys_computer,=“,no,”,IF,age,=“40”AND,credit_rating,=“,excellent,”,THEN,buys_computer,=“,yes,”,IF,age,=“=30”AND,credit_rating,=“,fair,”,THEN,buys_computer,=“,no,”,Avoid Overfitting in Classification,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 earlydo 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”treeget a sequence of progressively pruned trees,Use a set of data different from the training data to decide which is the“best pruned tree”,Approaches to Determine the Final Tree Size,Separate training(2/3)and testing(1/3)sets,Use cross validation,Use all the data for training,but apply a,statistical test,(e.g.,chi-square)to estimate whether expanding or pruning a node may improve the entire distribution,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,Classificationa 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,(EDBT96 Mehta et al.),builds an index for each attribute and only class list and the current attribute list reside in memory,SPRINT,(VLDB96 J.Shafer et al.),constructs an attribute list data structure,PUBLIC,(VLDB98 Rastogi&Shim),integrates tree splitting and tree pruning:stop growing the tree earlier,RainForest,(VLDB98 Gehrke,Ramakrishnan&Ganti),separates the scalability aspects from the criteria that determine the quality of the tree,builds an AVC-list(attribute,value,class label),Presentation of Classification Results,Visualization of a,Decision Tree,in SGI/MineSet 3.0,Interactive Visual Mining,by Perception-Based Classification(PBC),Bayesian Classification:Why?,Probabilistic learning,:Calculate explicit probabilities for hypothesis,among the most practical approaches to certain types of learning problems,Incremental,:Each training example can incrementally increase/decrease the probability that a hypothesis is correct.Prior knowledge can be combined with observed data.,Probabilistic prediction,:Predict multiple hypotheses,weighted by their probabilities,Standard,:Even when Bayesian methods are computationally intractable,they can provide a standard of optimal decision making against which other methods can be measured,Bayesian Theorem:Basics,Let,X,be a data sample whose class label is unknown,Let,H,be a hypothesis that,X,belongs to class,C,For classification problems,determine,P(H|X),:the probability that the hypothesis holds given the observed data sample,X,P(H):,prior probability of hypothesis,H,(i.e.the initial probability before we observe any data,reflects the background knowledge),P(X),:probability that sample data is observed,P(X|H),:probability of observing the sample,X,given that the hypothesis holds,Bayesian Theorem,Given training data,X,posteriori probability of a hypothesis,H,P(H|X),follows the Bayes theorem,Informally,this can be written as,posteriori=likelihood x prior/evidence,MAP(maximum posteriori)hypothesis,Practical difficulty:require initial knowledge of many probabilities,significant computational cost,Nave Bayes Classifier,A simplified assumption:attributes are conditionally independent:,The product of occurrence of say 2 elements,x,1,and,x,2,given the current class is,C,is the product of the probabilities of each element taken separately,given the same class,P(y,1,y,2,C)=P(y,1,C)*P(y,2,C),No dependence relation between attributes,Greatly reduces the computation cost,only count the class distribution.,Once the probability,P(X|C,i,),is known,assign,X,to the class with maximum,P(X|C,i,)*P(C,i,),Training dataset,Class:,C1:buys_computer=,yes,C2:buys_computer=,no,Data sample,X=(age=30,Income=medium,Student=yes,Credit_rating=,Fair),Nave Bayesian Classifier:An Example,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 0.0.667=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”,Nave Bayesian 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 Nave Bayesian Classifier,How to deal with these dependencies?,Bayesian Belief Networks,Bayesian Belief Networks,Bayesian belief network allows a,subset,of the variables conditionally independent,A graphical model of causal relationships,Represents,dependency,among the variables,Gives a specification of joint probability distribution,Nodes:random variables,Links:dependency,X,Y,are the parents of,Z,and,Y,is the parent of,P,No dependency between,Z,and,P,Has no loops or cycles,Bayesian Belief Network:An Example,Family,History,LungCancer,PositiveXRay,Smoker,Emphysema,Dyspnea,LC,LC,(FH,S),(FH,S),(FH,S),(FH,S),0.8,0.2,0.5,0.5,0.7,0.3,0.1,0.9,Bayesian Belief Networks,The conditional probability table for the variable LungCancer:,Shows the conditional probability for each possible combination of its parents,Learning Bayesian Networks,Several cases,Given both the network structure and all variables observable:learn only the CPTs,Network structure known,some hidden variables:method of gradient descent,analogous to neural network learning,Network structure unknown,all variables observable:search through the model space to reconstruct graph topology,Unknown structure,all hidden variables:no good algorithms known for this purpose,D.Heckerman,Bayesian networks for data mining,What Is Prediction?,(Numerical)prediction is similar to classification,construct a model,use model to predict continuous or ordered value for a given input,Prediction is different from classification,Classification refers to predict categorical class label,Prediction models continuous-valued functions,Major method for prediction:regression,model the relationship between one or more,independent,or,predictor,variables and a,dependent,or,response,variable,Regression analysis,Linear and multiple regression,Non-linear regression,Other regression methods:generalized linear model,Poisson regression,log-linear models,regression trees,Linear Regression,Linear regression,:involves a response variable y and a single predictor variable x，,y=,w,0,+w,1,x,where w,0,(y-intercept)and w,1,(slope)are regression coefficients,Method of least squares,:estimates the best-fitting straight line,Multiple linear regression,:involves more than one predictor variable,Training data is of the form(,X,1,y,1,),(,X,2,y,2,),(,X,|D|,y,|D|,),Ex.For 2-D data,we may have:y=,w,0,+w,1,x,1,+w,2,x,2,Solvable by extension of least square method or using SAS,S-Plus,Many nonlinear functions can be transformed into the above,Some nonlinear models can be modeled by a polynomial function,A polynomial regression model can be transformed into linear regression model.For example,y=,w,0,+w,1,x+w,2,x,2,+w,3,x,3,convertible to linear with new variables:,x,2,=x,2,x,3,=x,3,y=,w,0,+w,1,x+w,2,x,2,+w,3,x,3,Other functions,such as power function,can also be transformed to linear model,Some models are intractable nonlinear(e.g.,sum of exponential terms),possible to obtain least square estimates through extensive calculation on more complex formulae,Nonlinear Regression,Generalized linear model,:,Foundation on which linear regression can be applied to modeling categorical response variables,Variance of y is a function of the mean value of y,not a constant,Logistic regression,:models the prob.of some event occurring as a linear function of a set of predictor variables,Poisson regression,:models the data that exhibit a Poisson distribution,Log-linear models,:(for categorical data),Approximate discrete multidimensional prob.distributions,Also useful for data compression and smoothing,Regression trees and model trees,Trees to predict continuous values rather than class labels,Other Regression-Based Models,Regression Trees and Model Trees,Regression tree:proposed in CART system(Breiman et al.1984),CART:Classification And Regression Trees,Each leaf stores a,continuous-valued prediction,It is the,average value of the predicted attribute,for the training tuples that reach the leaf,Model tree:proposed by Quinlan(1992),Each leaf holds a regression modela multivariate linear equation for the predicted attribute,A more general case than regression tree,Regression and model trees tend to be more accurate than linear regression when the data are not represented well by a simple linear model,Predictive modeling:Predict data values or construct generalized linear models based on the database data,One can only predict value ranges or category distributions,Method outline:,Minimal generalization,Attribute relevance analysis,Generalized linear model construction,Prediction,Determine the major factors which influence the prediction,Data relevance analysis:uncertainty measurement,entropy analysis,expert judgement,etc.,Multi-level prediction:drill-down and roll-up analysis,Predictive Modeling in Multidimensional Databases,Prediction:Numerical Data,Prediction:Catego