Immunity-Based Computational Models - Immunological Computation: Theory and Applications - page 55

of all the available bits are used in matching two strings, in the rcb rule. Here, also
the size of a window needs to be specifi ed. In an N -dimensional space, the partial
distance between x and y , for a window size w , is defi ned as

w

∑

2

dxy (, ) ( x y )

s s

i i

i 1

where s i belongs to {1, 2, …, N }.

3.3.8.3 Minkowski Distance
It is also known as λ -norm distance, and it is defi ned as

1

( )

∑

dxy (, ) x y

i i

=

When λ 1, it becomes the Manhattan distance, also known as the city block

distance. If λ

=

2, it is equivalent to a Euclidean distance.

3.3.8.4 Chebyshev Distance

It is also known as the infi nity norm distance, denoted by D ∞ , and it is defi ned as
the maximum of the diff erences for all features

= - =

d ( x , y ) max{ | x i y i | for i 1, …, n }

3.3.9 Mixed Representation

Some distance measure defi ned for mixed data, that is, continuous and categorical
data, are explained in the following sections.

3.3.9.1 Heterogeneous Euclidean-Overlap Metric

Heterogeneous Euclidean-overlap metric (HEOM) distance is defi ned for mixed
data, that is, continuous and categorical data.

N

∑

2

HEOM (, ) xy heom ( x y )

i i

i 1