Immunity-Based Computational Models - Immunological Computation: Theory and Applications - page 51

1 , if X 1 , Y 0 N

i i

∑

b ,

i i

0 , otherwise

i 1

1 , if X 0 , Y 1 N

i i

∑

c ,

i i

0 , otherwise

i 1

1 , if XY 0

N

i i

∑

d ,

i i

0 , otherwise

i 1

X i and Y i denote the i th bit of string x and y , respectively; a counts the number of
1s that match at the same positions of both strings; similarly, d counts the number
of 0s that match at the same positions of both strings; b counts the number of 1s
in string x that do not match string y ; and c counts the number of 0s in string x
that do not match string y . h ese values are combined to defi ne diff erent similarity
functions as follows:

1. Russel and Rao

a
abcd

f

2. Jacard and Needham

a
abc

f

3. Kulzinski

a
bc

f

1

4. Sokal and Michener

ad
abcd

f