Page 179 - Introduction to Statistical Pattern Recognition

4 Parametric Classifiers 161

In IC1 =In lrl IRI lrl

n
=xln0,2+1n IRI. (4.125)
i=l
Thus, we can focus our attention on R-‘ and In IR I. A particular form of the
toeplitz matrix, (3.13), has the closed forms for the inverse and determinant as
seen in (3.14) and (3.15). Rewritting these.

(4.126)

1 -P 0 ... 0

-p l+p2 . .

0 . 0 (4.127)

1+p* -p

0 ... 0 -P 1

I R I = (1 - p2)”-I (4.128)

Thus, using (4.126) as the form to approximate the correlation matrix,
the estimation process of an approximated covariance matrix is given as fol-
lows:
-2
(1) Estimate O’ by the sample variance, bi .
A
by
(2) Estimate c;,;+~ = pi,i+loioi+l the sample covariance, c;.;+~, and
I
A,.
divide ci.i+l by oioi+l to obtain the estimate of A