Introduction to Pattern Recognition: A Matlab Approach

2.3 The Sum of Error Squares Classifier 39

In a similar manner, produce X

2

. Take the following steps:

Step 1. To compute the condition number of X

1

X

T

1

and the solution vector w for the original version of

the LS classifier, type

cond_num=cond(X1*X1')

w=SSErr(X1,y1,0)

Step 2. To repeat step 1 for the regularized version of the LS classifier, type

C=0.1;

cond_num=cond(X1*X1'+C*eye(l+1))

w=SSErr(X1,y1,C)

Step 3. Observe that the condition number of X

1

X

T

1

(1.4767 ×10

17

) is orders of magnitude greater

than that of X

1

X

T

1

+CI (9.3791 ×10

4

), where I is the (l +1) ×(l +1) identity matrix. In the

original version (C = 0), and for the current MATLAB working precision,