Transcript Introduction to Pattern Recognition

Introduction to Pattern Recognition
The 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 Distributions
X=-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[-(xu)^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
Vd 

d /2
( d / 2  1)
( x  1)  x( x )
d
r ,