《模式识别 Pattern Recognition》课程教学资源（PPT课件讲稿）Sergios Theodoridis Konstantinos Koutroumbas

A Course on PATTERN RECOGNITION Sergios Theodoridis KonstantinosKoutroumbas Version 3 日

1 Sergios Theodoridis Konstantinos Koutroumbas Version 3

PATTERN RECOGNITON typical application areas Machine vision Character recognition(OCR) Computer aided diagnosis Speech /Music/Audio recognition Face recognition Biometrics Image data Base retrieval Data mining Social Networks Bionformatics The task: Assign unknown objects- patterns -into the correct cass. This is known as classification

2 PATTERN RECOGNITION ❖ Typical application areas ➢ Machine vision ➢ Character recognition (OCR) ➢ Computer aided diagnosis ➢ Speech/Music/Audio recognition ➢ Face recognition ➢ Biometrics ➢ Image Data Base retrieval ➢ Data mining ➢ Social Networks ➢ Bionformatics ❖ The task: Assign unknown objects – patterns – into the correct class. This is known as classification

Features: These are measurable quantities obtained from the patterns and the classification task is based on their respective values. Feature vectors: a number of features X 15°l constitute the feature vector X=IX R Feature vectors are treated as random vectors

3 ❖ Features: These are measurable quantities obtained from the patterns, and the classification task is based on their respective values. ❖Feature vectors: A number of features constitute the feature vector Feature vectors are treated as random vectors. ,..., , 1 l x x   T l x = x1 ,..., xl R

An example

4 An example:

. the classifier consists of a set of functions whose values computed at x, determine the class to which the corresponding pattern belongs Classification system overview Patterns sensor feature generation feature selection classifier design system L evaluation

5 ❖ The classifier consists of a set of functions, whose values, computed at , determine the class to which the corresponding pattern belongs ❖ Classification system overview x sensor feature generation feature selection classifier design system evaluation Patterns

8 Supervised -unsupervised semisupervised pattern recognition The major directions of learning are Supervised Patterns whose class is known a-priori are used for training Unsupervised: The number of classes/groups is(in general)unknown and no training patterns are available Semisupervised: a mixed type of patterns is available. For some of them their corresponding class is known and for the rest is not

6 ❖ Supervised – unsupervised – semisupervised pattern recognition: The major directions of learning are: ➢ Supervised: Patterns whose class is known a-priori are used for training. ➢ Unsupervised: The number of classes/groups is (in general) unknown and no training patterns are available. ➢ Semisupervised: A mixed type of patterns is available. For some of them, their corresponding class is known and for the rest is not

CLASSIFTERS BASED ON BAYES DECISION THEORY Statistical nature of feature vectors x=[x,x2…,x丁 8 assign the pattern represented by feature vector x to the most probable of the available classes a122…OM That is x=>@: P(o,lx) maximum

7 CLASSIFIERS BASED ON BAYES DECISION THEORY ❖ Statistical nature of feature vectors ❖ Assign the pattern represented by feature vector to the most probable of the available classes That is maximum   T 1 2 l x = x ,x ,...,x x 1 ,2 ,..., M x : P( x) →i i

Computation of a-posteriori probabilities >Assume known a-priori probabilities P(1),P(O2)…P(O4) p(a,),i=1, 2,,M This is also known as the likelihood of xF·toO

8 ❖ Computation of a-posteriori probabilities ➢ Assume known • a-priori probabilities • This is also known as the likelihood of ( ), ( )..., ( ) P 1 P 2 P  M p(xi ),i =1,2,...,M . . . i x wr to 

The bayes rule(m=2) P(x)P(ox)=p(xo )P(a,)= (@, p(xO)P(O) Where p(x)=∑p(xo)P()

9 = = = =  2 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) i i i i i i i i i p x p x P p x p x P P x p x P x p x P         ➢ The Bayes rule (Μ=2) where

The Bayes classification rule(for two classes M=2) Given x classify it according to the rule P(ax)>P(a2x)x→a fP(a2)>P(a|x)x→O s equivalently: classify x according to the rule P(a)P(a)(<p(xa)P(a) For equiprobable classes the test becomes P(xo(p(xo2

10 ❖ The Bayes classification rule (for two classes M=2) ➢ Given classify it according to the rule ➢ Equivalently: classify according to the rule ➢ For equiprobable classes the test becomes x 2 1 2 1 2 1 ( ) ( ) ( ) ( )        →  → P x P x x P x P x x If If ( ) ( )( ) ( ) ( ) 1 1 2 P 2 p x P  p x ( )( ) ( ) 1 2 p x  p x x