Page 99 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

Chapter 3

NUMERICAL LINEAR ALGEBRA
Algorithm Collections

1. HOTELLING TRANSFORMATION

Consider the set of n-dimensional vectors collected in which the elements of
the vector are dependent to each other (i.e.) the covariance matrix computed
for the collected vectors are not the diagonal matrix. The co-variance matrix
is computed as follows.
Let x 1, x 2,…x m be the collection of ‘m’, ‘n-dimensional vectors. The
T
T
T
co-variance matrix is computed using E[(X-µ x) (X-µ x) ] = E(XX )- µ x µ x ,
where µ x is the mean vector computed using the collected vectors (ie)
µ x=[x 1+x 2+x 3+…x m]/m.
Hotelling Transformation transforms the set of vectors x 1, x 2,…x m into
another set of vectors (ie) y 1, y 2,…y m, such that the covariance matrix
computed for the transformed vectors is diagonal in nature.

Covariance Matrix (CM) a 1 b 1 c 1 d 1
b 1 b 2 c 2 d 2
c 1 c 2 c 3 d 3
d 1 d 2 d 3 d 4

87