Page 192 - Introduction to Statistical Pattern Recognition

174 Introduction to Statistical Pattern Recognition

1 2'1-1
- ZXkj = 0, (4.158)
2" j*

, 2'1-1
- = 1 , (4.159)
2"
J*

(4.160)

where xkj is either +1 or -1. Thus, if we define the sample matrix as

(4.161)

2"

then the row vectors of U are mutually orthonormal, that is

UUT = 2"1 . (4.162)

Example 7: Table 4-2 shows an example of three binary inputs. We
can easily see that (4.158)-(4.162) are all satisfied.
Let y(X) be the desired output of a pattern recognition network for the
input X. The y(X) is not necessarily a binary number. One of the design
procedures which may be used to realize this network by a linear discriminant
function is to minimize the mean-square error between y(X) and V'X + v,,.
The mean-square error can be expressed by

where W and r are the same as the ones used in (4.78). Therefore, the W
which minimizes E' is