Immunity-Based Computational Models - Immunological Computation: Theory and Applications - page 54

3.3.7 R-Chunk Matching Rule

Balthrop et al. (2002) introduced a generalization of rcb matching rule called r -chunk
matching rule. As in rcb matching rule, a detector is specifi ed by a binary string c and
parameter r . An r -chunk detector d is said to match a string x if all bits of c are equal
to the r bits of x in the window specifi ed by c . In contrast to the rcb matching rule, the
r -chunk approach allows the use of detectors of any size. h is fact has an improvement
on the ability of the detectors to cover the self-space. h e diff erence from rcb rule is
that the matching window is specifi ed for each individual detector. A group of r -chunk
detectors that cover all possible windows has the same eff ect as an rcb detector.
In mathematical terms, x

= =

e 1 e 2 … e m (an element in the shape-space) and d

≤ ≤ − +

( p ; d 1 d 2 … d r ) with r m , p m r 1 match according to the r -chunk rule if and

= = + −

only if e i 1. In other words, element x matches detector d

if, at position p , there is a sequence of length r where all the characters are identical.

d i for i p , …, p r

3.3.8 Real-Valued Vector Matching Rules

Some distance measures that have been used to defi ne matching rules in real-valued
vector representation are explained in the following sections.

3.3.8.1 Euclidean Distance

A Euclidean distance is defi ned as

( )

∑

2

dxy (, ) x y x y

i i

i

Euclidean distance can be modifi ed when all the dimensions do not have equal
weights by multiplying each component of the vectors by specifi c weights. Other
distance measures can be used to defi ne real-valued matching rule in a similar way
to Euclidean distance. h e choice of distance measures mainly relies on the type of
data and domain knowledge of the specifi c application. Several distance measures
summarized by Hamaker and Boggess (2004) are presented in the following
sections.

3.3.8.2 Partial (Euclidean) Distance

It is a variation of the Euclidean distance, and it is defi ned over some elements of
a vector, as opposed to the whole vector. It is equivalent to the Euclidean distance
projected on a lower dimensional subspace of the original space. In other words,
the Euclidean distance is not calculated over all the elements of the vector, but it is
calculated taking into account only some elements. h is is similar to the way some