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On the Use of Hyperspheres in Artificial
Immune Systems as Antibody
Recognition Regions
Thomas Stibor
1
, Jonathan Timmis
2
, and Claudia Eckert
1
1
Department of Computer Science
Darmstadt University of Technology
{stibor, eckert}@sec.informatik.tu-darmstadt.de
2
Departments of Electronics and Computer Science
University of York, Heslington, York
jtimmis@cs.york.ac.uk
Abstract.
Using hyperspheres as antibody recognition regions is an es-
tablished abstraction which was initially proposed by theoretical immu-
nologists for use in the modeling of antibody-antigen interactions. This
abstraction is also employed in the development of many artificial im-
mune system algorithms. Here, we show several undesirable properties
of hyperspheres, especially when operating in high dimensions and dis-
cuss the problems of hyperspheres as recognition regions and how they
have affected overall performance of certain algorithms in the context of
real-valued negative selection.
1
Introduction
Work in theoretical immunology has developed various representations for the
interactions between antibody and antigen, and anity metrics for modeling
these such interactions. These antibody-antigen binding models were proposed
for describing antibody cross-reactivity and multi-specificity [1] or for estimating
the antibody repertoire size [2]. This work has provided much of the foundations
for the development of artificial immune system (AIS) [3].
AIS is a paradigm inspired by the immune system and is used for solving
computational and information processing problems. AIS exploit principles and
methods developed by theoretical and experimental immunology, and abstract
certain properties which can be implemented in computational systems [3]. In
this paper, the abstraction we will consider is the hypersphere. This abstrac-
tion of hyperspheres has been used in many artificial immune system algorithms
which have been applied to many areas such as anomaly detection, pattern recog-
nition and clustering problems [4,5,6,7,8,9]. In this paper we describe mathemat-
ical properties of hyperspheres, which manifest themselves in high-dimensional
space, and we provide suggestions on the applicability of hyperspheres as recog-
nition units. Moreover we discuss the applicability of hyperspheres in the context
of real-valued negative selection and explain reported poor classification results
shownin[6].
