模式识别讲座课件

1Pattern RecognitionNanyang Technological UniversityDr.Shi,DamingHarbin Engineering University标题添加点击此处输入相关文本内容点击此处输入相关文本内容总体概述点击此处输入相关文本内容标题添加点击此处输入相关文本内容3What is Pattern RecognitionnClassify raw data into the category of the pattern.nA branch of artificial intelligence concerned with the identification of visual or audio patterns by computers.For example character recognition,speech recognition,face recognition,etc.nTwo categories:syntactic(or structural)pattern recognition and statistical pattern recognitionIntroductionPattern Recognition=Pattern Classification45What is Pattern RecognitionTraining PhaseTraining dataUnknown dataFeature ExtractionLearning(Feature selection,clustering,discriminant function generation,grammar parsing)Recognition(statistical,structural)ResultsRecognition PhaseKnowledge6What is Pattern RecognitionTraining PhaseTraining dataUnknown dataFeature ExtractionLearning(Feature selection,clustering,discriminant function generation,grammar parsing)Recognition(statistical,structural)ResultsRecognition PhaseKnowledge7CategorisationnBased on Application AreasnFace RecognitionnSpeech RecognitionnCharacter Recognitionnetc,etcnBased on Decision Making ApproachesnSyntactic Pattern RecognitionnStatistical Pattern RecognitionIntroduction8Syntactic Pattern RecognitionAny problem is described with formal language,and the solution is obtained through grammatical parsingIn Memory of Prof.FU,King-Sun and Prof.Shu WenhaoIntroduction9Statistical Pattern RecognitionIn the statistical approach,each pattern is viewed as a point in a multi-dimensional space.The decision boundaries are determined by the probability distribution of the patterns belonging to each class,which must either be specified or learned.Introduction10Scope of the SeminarnModule 1 Distance-Based ClassificationnModule 2 Probabilistic ClassificationnModule 3 Linear Discriminant AnalysisnModule 4 Neural Networks for P.R.nModule 5 ClusteringnModule 6 Feature SelectionIntroduction11Module 1 Distance-Based ClassificationNanyang Technological UniversityDr.Shi,DamingHarbin Engineering UniversityPattern Recognition12OverviewnDistance based classification is the most common type of pattern recognition techniquenConcepts are a basis for other classification techniquesnFirst,a prototype is chosen through training to represent a classnThen,the distance is calculated from an unknown data to the class using the prototypeDistance-Based Classification13Classification by distanceObjects can be represented by vectors in a space.In training,we have the samples:In recognition,an unknown data is classified by distance:Distance-Based Classification14PrototypenTo find the pattern-to-class distance,we need to use a class prototype(pattern):(1)Sample Mean.For class ci,(2)Most Typical Sample.chooseSuch thatis minimized.Distance-Based Classification15Prototype Nearest Neighbour(3)Nearest Neighbour.chooseSuch thatis minimized.Nearest neighbour prototypes are sensitive to noise and outliers in the training set.Distance-Based Classification16Prototype k-NN(4)k-Nearest Neighbours.K-NN is more robust against noise,but is more computationally expensive.The pattern y is classified in the class of its k nearest neighbours from the training samples.The chosen distance determines how near is defined.Distance-Based Classification17Distance MeasuresnMost familiar distance metric is the Euclidean distancenAnother example is the Manhattan distance:nMany other distance measures Distance-Based Classification18Minimum Euclidean Distance(MED)ClassifierEquivalently,19Decision BoundaryGiven a prototype and a distance metric,it is possible to find the decision boundary between classes.Linear boundaryNonlinear boundaryDecision Boundary=Discriminant FunctionDistance-Based Classificationlightnesslengthlightnesslength20ExampleDistance-Based Classification21ExampleAny fish is a vector in the 2-dimensional space of width and lightness.21xxfishDistance-Based Classificationlightnesslength22ExampleDistance-Based Classification23SummarynClassification by the distance from an unknown data to class prototypes.nChoosing prototype:nSample MeannMost Typical SamplenNearest NeighbournK-Nearest NeighbournDecision Boundary=Discriminant FunctionDistance-Based Classification24Module 2 Probabilistic ClassificationNanyang Technological UniversityDr.Shi,DamingHarbin Engineering UniversityPattern Recognition25Review and Extend26Maximum A Posterior(MAP)ClassifiernIdeally,we want to favour the class with the highest probability for the given pattern:Where P(Ci|x)is the a posterior probability of class Ci given x27Bayesian ClassificationnBayes Theoreom:Where P(x|Ci)is the class conditional probability density(p.d.f),which needs to be estimated from the available samples or otherwise assumed.Where P(Ci)is a priori probability of class Ci.Probabilistic Classification28MAP ClassifiernBayesian Classifier,also known as MAP ClassifierSo,assign the pattern x to the class with maximum weighted p.d.f.Probabilistic Classification29Accuracy VS.RiskHowever,in the real world,life is not just about accuracy.In some cases,a small misclassification may result in a big disaster.For example,medical diagnosis,fraud detection.The MAP classifier is biased towards the most likely class.maximum likelihood classification.Probabilistic Classification30Loss FunctionOn the other hand,in the case of P(C1)P(C2),the lowest error rate can be attained by always classifying as C1A solution is to assign a loss to misclassification.which leads to Also known as the problem of imbalanced training data.Probabilistic Classification31Conditional RiskInstead of using the likelihood P(Ci|x),we use conditional riskcost of action i given class j To minimize overall risk,choose the action with the lowest risk for the pattern:Probabilistic Classification32Conditional RiskProbabilistic Classification33ExampleAssuming that the amount of fraudulent activity is about1%of the total credit card activity:C1=Fraud P(C1)=0.01C2=No fraud P(C2)=0.99If losses are equal for misclassification,then:Probabilistic Classification34ExampleHowever,losses are probably not the same.Classifying a fraudulent transaction as legitimate leads to direct dollar losses as well as intangible losses(e.g.reputation,hassles for consumers).Classifying a legitimate transaction as fraudulent inconveniences consumers,as their purchases are denied.This could lead to loss of future business.Lets assume that the ratio of loss for not fraud to fraud is 1 to 50,i.e.,A missed fraud is 50 times more expensive than accidentally freezing a card due to legitimate use.Probabilistic Classification35ExampleBy including the loss function,the decision boundaries change significantly.Instead of We use Probabilistic Classification36Probability Density FunctionRelatively speaking,its much easy to estimate a priori probability,e.g.simply takekkiiNNCP)(To estimate p.d.f.,we can(1)Assume a known p.d.f,and estimate its parameters(2)Estimate the non-parametric p.d.f from training samplesProbabilistic Classification37Maximum Likelihood Parameter EstimationnWithout the loss of generality,we consider Gaussian density.P(x|Ci)=Training examples for class CiParameter values to be identifiedWe are looking forthat maximize the likelihood,so,The sample covariance matrix!38Density Estimationnif we do not know the specific form of the p.d.f.,then we need a different density estimation approach which is a non-parametric technique that uses variations of histogram approximation.(1)Simplest density estimation is to use“bins”.e.g.,in 1-D case,take the x-axis and divide into bins of length h.Estimate the probability of a sample in each bin.kN is the number of samples in the bin(2)Alternatively,we can take windows of unit volume and apply these windows to each sample.The overlap of the windows defines the estimated p.d.f.This technique is known as Parzen windows or kernels.Probabilistic Classification39SummarynBayesian Theoreom nMaximum A Posterior Classifier=Maximum Likelihood classifernDensity EstimationProbabilistic Classification40Module 3 Linear Discriminant AnalysisNanyang Technological UniversityDr.Shi,DamingHarbin Engineering UniversityPattern Recognition41Linear Classifier-1A linear classifier implements discriminant function or a decision boundary represented by a straight line in the multidimensional space.Given an input,x=(x1 xm)Tthe decision boundary of a linear classifier is given by a discriminant functionWith weight vector w=(w1 wm)TbxwbxfmkkkT1)(xwLDA42Linear Classifier-2The output of the function f(x)for any input will depend upon the value of weight vector and input vector.For example,the following class definition may be employed:If f(x)0 Then x is Ballet dancerIf f(x)0 Then x is Rugby playerLDA43Linear Classifier-3bxfTxw)(x1x2f(x)0f(x)pel is cytoplasmIf value pel is nucleusthis is clustering based on density estimation.peaks=cluster centres.valleys=cluster boundariesClustering63Parameterized Density EstimationWe shall begin with parameterized p.d.f.,in which the only thing that must be learned is the value of an unknown parameter vectornWe make the following assumptions:nThe samples come from a known number c of classesnThe prior probabilities P(j)for each class are known nP(x|j,j)(j=1,c)are knownnThe values of the c parameter vectors 1,2,c are unknownClustering64Mixture DensitynThe category labels are unknown,and this density function is called a mixture density,andnOur goal will be to use samples drawn from this mixture density to estimate the unknown parameter vector.nOnce is known,we can decompose the mixture into its components and use a MAP classifier on the derived densities.tc21c1jparameters mixingjdensities componentjj),.,(where)(P.),|x(P)|x(P Clustering65Chinese Ying-Yang PhilosophynEverything in the universe can be viewed as a product of a constant conflict between the opposites Ying and Yang.YingnegativefemaleinvisiblepositivemalevisibleYangn The optimal status is reached if Ying-Yang achieves harmonyClustering66Bayesian Ying-Yang ClusteringnTo find a clusters y to partition input data xnx is visible but y is invisiblenx decides y in training but y decides x in runningp(x,y)=p(y|x)p(x)p(x,y)=p(x|y)p(y)xyp(,)Clustering67Bayesian Ying Yang Harmony Learning(1)nTo minimise the difference between the Ying-Yang pair:)()|(),(xpxypMMKLYangMYangYingdxdyypyxpxpxypYingYangMM)()|()()|(lndxdymxGxpxypyyyMYang),()()|(lnnTo select the optimal model(cluster number):)()(minargkJkHkkwherekyyykyyNikykJxypxypNkH1111lnln)()|(ln)|(1)(Clustering68Bayesian Ying Yang Harmony Learning(2)nParameter learning using EM algorithmnE-Step:nM-Step:1(,)(|)(,)jjjjyyyjjikjjjjyyyyG xmP yxG xm111(,)11(|)(,)jjjjjNNyyyjnewjjyikiijjjjyyyyG xmP yxNNG xm111(|)1(|)(|)NjjjiiNjnewjjjiyiiNjjjiyiiP yx xmP yx xNP yx211(|)()NjnewjjjjyiiyjiyP yxxmNClustering69SummarynClustering by DistancenGoodness of paretitioningnK-meansnClustering by Density EstimationnBYYClustering70Module 6 Feature SelectionNanyang Technological UniversityDr.Shi,DamingHarbin Engineering UniversityPattern Recognition71MotivationFeature SelectionClassifier performance depend on a combination of the number of samples,number of features,and complexity of the classifier.Q1:The more samples,the better?Q2:The more features,the better?Q3:The more complex,the better?However,the number of samples is fixed when trainingBoth requires to reduce the number of features72Curse of Dimensionalityif the number of training samples is small relative to the number of features,the performance may be degraded.Because:with the increase of the number of features,the number of unknown parameters will be increased accordingly,then the reliability of the parameter estimation decreases.Feature Selection73Ocams Razor Hypothesisor plurality should not be posited without necessity.Pluralitas non est ponenda sine neccesitate-William of Ockham(ca.1285-1349).To make the system simpler,unnecessary features must be removed.Feature Selection74Feature SelectionIn general,we would like to have a classifier to use a minimum number of dimensions,in order to achieve:-less computations-statistical estimation reliabilityFeature Selection:Given m measurements,choose nm best as featureWe require:A criterion to evaluate featuresAn algorithm to optimize the criterionFeature Selection75CriterionTypically,Interclass Distance(normalized by intraclass distance)2 classes:where mi1=mean of ith feature of class 1 si1=scatter(variance)of ith feature in class 1k classes:Feature Selection76OptimizingnChoosing n features from m measurements,the combinations are nUsually an exhaustive comparison is not feasible.nSome sub-optimal strategies include:nRank features by effectiveness and choose bestnIncrementally add features to set of chosen featuresnSuccessively add and delete features to chosen setFeature Selection问题提问与解答问答HERE COMES THE QUESTION 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