Introduction to Pattern Recognition: A Matlab Approach

118 CHAPTER 4 Feature Selection

Three class-separability measures are considered: divergence (implemented by the MATLAB func-

tion divergence), Bhattacharyya distance (divergenceBhata), and scatter matrices (ScatterMatrices).

4.7.1 Divergence

The definition of the divergence measure, for the general case, can be found in [Theo 09, Section 5.6].

Assume that we are given two normally distributed classes in the l-dimensional space. The divergence

between them is defined as

d

1,2

=

1

2

trace



S

−1

1

S

2

+S

−1

2

S

1

−2I



+

1

2

(m

1

−m

2

)

T



S

−1

1

+S

−1

2



(m

1

−m

2

) (4.4)

where S

i

is the covariance matrix; m

i

, i =1, 2 is the respective mean vector of the ith class; and I is the

l×l identity ...