-
8/2/2019 AASHISH TYAGI.
1/14
LOVELY PROFESSIONAL
UNIVERSITY
NAME: AASHISH TYAGI
CLASS:RK2904 ROLL NO:B45
REG. NO:10905843
SUBJECT:ARTIFICIAL INTELLIGENCE
-
8/2/2019 AASHISH TYAGI.
2/14
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.
-
8/2/2019 AASHISH TYAGI.
3/14
A Pattern Recognition Paradigm
-
8/2/2019 AASHISH TYAGI.
4/14
Texture Discrimination
-
8/2/2019 AASHISH TYAGI.
5/14
Shape Discrimination
-
8/2/2019 AASHISH TYAGI.
6/14
Optical Character Recognition
-
8/2/2019 AASHISH TYAGI.
7/14
Face Recognition & Discrimination
-
8/2/2019 AASHISH TYAGI.
8/14
Are They From the Same Person?
-
8/2/2019 AASHISH TYAGI.
9/14
-
8/2/2019 AASHISH TYAGI.
10/14
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
-
8/2/2019 AASHISH TYAGI.
11/14
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
-
8/2/2019 AASHISH TYAGI.
12/14
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]')
-
8/2/2019 AASHISH TYAGI.
13/14
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]')
-
8/2/2019 AASHISH TYAGI.
14/14
Volumes of Unit Spheres
/2
,( / 2 1)
( 1) ( )
d
ddV r
d
x x x
