Introduction to Pattern RecognitionThe applications of Pattern Recognition can be found everywhere. Examples include disease categorization, prediction of survival rates for patients of specific disease, fingerprint verification, face recognition,iris discrimination, chromosome shape discrimination, optical character recognition, texture discrimination, speech recognition, and etc. The design of a pattern recognition system should consider the application domain. A universally best pattern recognition system has never existed. This course will introduce the general concepts of Pattern Recognition (Supervised Learning) and Cluster Analysis (Unsupervised Learning) with examples in texture and shape discrimination. A project of applying the strategies of Pattern Recognition and Cluster Analysis to do Data Mining for interesting data sets acquired from Taiwanese Health Insurance Database or face image databases may be considered. The goal of visualization,prediction, and policy making to improve the life quality and security of Taiwanese people may be pursued if the data are available.

A Pattern Recognition Paradigm

Texture Discrimination

Shape Discrimination

Optical Character Recognition

Face Recognition & Discrimination

Are They From the Same Person?

Foundation of Mathematics

• LLt decomposition and eigenvalues and eigenvectors of nonnegative definite matrices

• Random variables and random vectors• Normal (Gaussian) Distributions• Covariance matrix of a random vector• Maximum Likelihood Estimation (MLE)• Volumes of unit spheres• Least squares problems

Computing Covariance Matrix

d=4; n=150;

fin=fopen('datairis.txt');

fgetl(fin); fgetl(fin); fgetl(fin);

A=fscanf(fin,'%f',[d+1 n]);

B=A';

X=B(:,1:d);

u=mean(X);

C=cov(X);

[V D]=eig(C);

sort(diag(D),'descend')

• Eigenvalues obtained from the left Matlab code for iris data set are

• 4.2282• 0.2427• 0.0782• 0.0238

Plot Gaussian DistributionsX=-3.6:0.1:3.6;u=0; v1=1; v2=0.5; v4=0.25; v8=0.125;Y1=1/sqrt(2*pi*v1)*exp(-(X-u).^2/(2*v1));Y2=1/sqrt(2*pi*v2)*exp(-(X-u).^2/(2*v2));Y4=1/sqrt(2*pi*v4)*exp(-(X-u).^2/(2*v4));Y8=1/sqrt(2*pi*v8)*exp(-(X-u).^2/(2*v8));plot(X,Y1,'r-',X,Y2,'g-',X,Y4,'b-',X,Y8,'m-')

legend('\sigma^2=1','\sigma^2=0.5','\sigma^2=0.25','\sigma^2=0.125',2)

title('f(x)= [1/(2\pi\sigma^2]^{1/2}*exp[-(x-u)^2/2\sigma^2]')

Plot a 2d Gaussian Distribution

x=-3.6:0.3:3.6;y=x';X=ones(length(y),1)*x;Y=y*ones(1,length(x));Z=exp((X.^2+Y.^2)/2+… eps)/(2*pi);mesh(Z);title('f(x,y)=(1/2\pi)*… exp[-(x^2+y^2)/2.0]')

Volumes of Unit Spheres

/2

,( / 2 1)

( 1) ( )

dd

dV rd

x x x