T Cell–Inspired Algorithms - Immunological Computation: Theory and Applications - page 89

Gonzalez et al. (2003b) assumed that the self-set ˆ consisted of a collection of
neighborhoods around each one of the self-sample points, S ; each neighborhood

is defi ned as a hypersphere of radius r s around a sample point. h erefore, the set Ŝ
may be defi ned as

′

ˆ : = ∈ ′

-

≤

{ x U : there exists s in S , || s x || r self }

and the volume of S ˆ is described as

∫

V : χ () x dx

S S

U

where

∈

1 if xS

S

:

0 if xS

Monte Carlo methods are well-established techniques with a strong mathematical
foundation used for volume estimation, and they are being used here to estimate
the coverage of a set of detectors. Also, this technique is useful in probabilistically
estimating the overlap among detectors with diff erent shapes, which otherwise will
be cumbersome if a geometrical approach is followed.
Figure 4.11 illustrates the generation of hyperspherical detectors using Monte
Carlo integration and simulated annealing.

Self-data

Generate random
population of
detectors

Optimize detector

Figure 4.11 A heuristic algorithm to generate hyperspherical negative detectors.