Introduction to Pattern Recognition: A Matlab Approach

3.5 The Kernel PCA 97

e=0;

end

end

t=sqrt(rˆ 2-sum(temp.ˆ 2))+noise_level*(rand-0.5);

qw=[temp t; temp -t]';

X=[X qw];

end

ThedatasetX

test

is generated similarly (use the value 100 as the seed for the rand function).

To define the class labels of the data vectors, type

[l,N]=size(X);

y=[ones(1,n_points(1)) -ones(1,n_points(2))];

y_test=[ones(1,n_points(1)) -ones(1,n_points(2))];

To pl ot the data set X, type

2

figure(1), plot3(X(1,y==1),X(2,y==1),X(3,y==1),'r.',...

X(1,y==-1),X(2,y==-1),X(3,y==-1),'b+')

figure(1), axis equal

X

test

is plotted similarly. Clearly, the two classes are nonlinearly separable.

Step 2. To perform kernel PCA with kernel exponent i al and ...