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Stevens Institute of Technology
Department of Electrical and Computer Engineering
CpE 646 Pattern Recognition and Classification
Homework 4
Problem 1: Once again we use the data set s “ hw3_2_1 ” and “ hw3_2_2 ” from
Homework 3. The sample vectors in “ hw3_2_1 ” are from class ω 1 and sample vectors in
“ hw3_2_2 ” are from class ω 2
Use k-nearest neighbor method to estimate the class conditional density functions p ( x | ω 1 )
and p ( x | ω 2 ) for every x in {-4:0.1:8, -4:0.1:8}; use “ mesh ” function in Matlab to plot the
results; and then classify x =[1,-2]
t
based on the estimation. Let k =10.
( Hint: The “sort” function in Matlab can be used to find the closest neighbors.)
clear all
clc
load ('hw3.mat')
label1=ones(1,100);
label2=1+label1;
label=[label1 label2];
data1=hw3_2_1;
data2=hw3_2_2;
[r,c]=size(data1);
train_data=[data1 data2];
P1=zeros(121,121);
P2=zeros(121,121);
K=10;
w=0;
for i=-4:0.1:
w=w+1;h=0;
for j=-4:0.1:
h=h+1;
ki=0;kj=0;
test_data=[i;j];
% calculate Euclid Distance
distance=zeros(1,200);
for x = 1:
a=i-train_data(1,x);
c=j-train_data(2,x);
distance(x)=sqrt(a.^2+c^2);
end
% fint the closet neighbors and choose K number
[dist,neighbors]=sort(distance);
dist =dist(1:K);
neighbors=neighbors(1:K);
% find the lable(class)
for k=1:K
if label(neighbors(k))==
ki=ki+1;
else kj=kj+1;
end
end
P1(w,h)=ki/K;
P2(w,h)=kj/K;
if i==1&&j==-
p1=P1(w,h)
p2=P2(w,h)
end
end
end
b=[-4:0.1:8];
mesh(b,b,P1)
hold on
mesh(b,b,P2)
2.2 Assume a function, which projects each input vector
1
1
2
2
1 2
to ˆ
x
x
x
x
x x
x x
plot
x ˆ in 3-D use Matlab function “plot3”.
clear all
clc
load ('hw4.mat')
data1=hw4_2_1;
data2=hw4_2_2;
data11=[data1;(data1(1,:)).*data1(2,:)];
data22=[data2;(data2(1,:)).*data2(2,:)];
plot3(data11(1,:),data11(2,:),data11(3,:),'*',data22(1,:),data22(2,:,:),data22(3,:),'o')
title('data set');
2.3 Now define an augmented vector as
1
2
1 2
x
x
x x
y x
. Use the Batch Perceptron
method (page 35 and 39, CPE646-9) to find the weight vector
0
1
2
3
a
a
a
a
a
in the
generalized linear discriminant function (page 22, 23. CPE646-9).
(Hint: let =1, =1, initialize
a y
clear all
clc
load ('hw4.mat')
data1=hw4_2_1;
data2=hw4_2_2;
%normalized
n=ones(1,100);
y1=[n;data1;(data1(1,:)).*data1(2,:)];
