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For developing competitive immune-inspired algorithms the antibody-antigen
representation and anity metric is a crucial parameter. We have found that
applying the abstraction of these hyperspheres for immune-inspired algorithms
can lead to poor results, especially for high-dimensional classification problems.
In this paper, we have shown that these hypersphere have undesirable prop-
erties in high dimensions — the volume tends to zero and nearly all uniformly
randomly distributed points are close to the hypersphere surface. We have pre-
sented these hypersphere properties andhaveprovidedanexplanationforpoor
classification results reported in [6]. In addition, we have now explained the lim-
itations of the real-valued negative selection for high-dimensional classification
problems, when employing hyperspheres. There is no reason to suggest that the
hypersphere properties we have discussed in this paper, are not valid obser-
vations for all high-dimensional classification problems where hyperspheres are
applied as recognition regions. Therefore, as a result, these adverse hypersphere
properties could bias all (artificial immune system) algorithms, which employ
hyperspheres as recognition units.
References
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