Immunity-Based Computational Models - Immunological Computation: Theory and Applications - page 48

h us, ε specifi es a recognition threshold; if the a nity between an antibody and an
antigen (X) is less than ε (i.e., the antigen lies inside the a nity region of an anti-
body), then the antigen is said to match (bind) the antibody (Balthrop et al., 2002).
3.1.1 RepresentationSchemes
h e entities involved in immune algorithms are mainly B- and T cells, antibodies,
and antigens. Representations that are used in most immune algorithms are
Binary strings
Strings over fi nite alphabets (other than binary)
Real-valued vectors
Hybrid representation where each entity consists of several features and each
feature may be of a diff erent type; for instance, integer, real value, boolean
value, or categorical information
h e binary representation, in general, can subsume other representations, that is,
any data type can be represented as a sequence of bits in the memory of a computer
(although their treatment diff ers). In theory, any matching rule defi ned on a high-
level representation can be expressed as a binary matching rule. Many models use
binary representation. Although binary string representation has some advantages
(any type of data can be represented in binary form, it is easy to analyze, and it is
good to represent categorical data), it also has limitations—it is di cult to interpret
in the original problem space, presents scalability issues, and is di cult to directly
apply on some conventional techniques that assume continuous spaces (Gonzalez et
al., 2003). h erefore, the other types of representations have been investigated for
use in immune algorithms (Stibor et al., 2005).
3.2 Affi nity Measures
To d e fi ne the notion of a nity between a T or B cell and an antigen, diff erent
similarity or distance measures are introduced. If a string representation is used, a
Hamming distance may be suitable. However, in the case of binary strings, other
distance measures have been used. Although a Euclidean distance may be used
when using a real-valued vector representation, other distance measures have also
been used.
A T cell is considered to detect foreign antigens in a certain region of the shape-
space. h is is due to the fact that antigen matching is not exact, but approximate.
h us, a T cell will match variations of a specifi c antigen. A T cell model is called
a detector; a detector is characterized by a set of attributes and a “matching rule,”
which is based on a distance measure (Gonzalez et al., 2003). Generally, a detector
can be implemented as either a production rule or a neural network or a software