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LOVELY PROFESSIONAL
UNIVERSITY
NAME: AASHISH TYAGI
CLASS:RK2904 ROLL NO:B45
REG. NO:10905843
SUBJECT:ARTIFICIAL INTELLIGENCE
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Introduction to Pattern Recognition
The applications of Pattern Recognition can be found everywhere.Examples include disease categorization, prediction of survival rates forpatients of specific disease, fingerprint verification, face recognition,iris discrimination, chromosome shape discrimination, optical characterrecognition, texture discrimination, speech recognition, and etc. The
design of a pattern recognition system should consider the applicationdomain. 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) withexamples in texture and shape discrimination. A project of applying thestrategies of Pattern Recognition and Cluster Analysisto do Data Mining
for interesting data sets acquired from Taiwanese Health Insurance Databaseor face image databases may be considered. The goal of visualization,prediction, and policy making to improve the life quality and security ofTaiwanese people may be pursued if the data are available.
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A Pattern Recognition Paradigm
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Texture Discrimination
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Shape Discrimination
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Optical Character Recognition
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Face Recognition & Discrimination
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Are They From the Same Person?
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Foundation of Mathematics
LLt decomposition and eigenvalues andeigenvectors of nonnegative 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
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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 obtainedfrom the left Matlab codefor iris data set are
4.2282
0.2427
0.0782
0.0238
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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[-(x-u)^2/2\sigma^2]')
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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]')
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Volumes of Unit Spheres
/2
,( / 2 1)
( 1) ( )
d
ddV r
d
x x x
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