This paper introduces hyper-ellipsoids as an improvement to hyper-spheres as intrusion detectors in a negative selection problem within an artificial immune system. Since hyper-spheres are a specialization of hyper-ellipsoids, hyper-ellipsoids retain the benefits of hyper-spheres. However, hyper-ellipsoids are much more flexible, mostly in that they can be stretched and reoriented. The viability of using hyper-ellipsoids is established using several pedagogical problems. We conjecture that fewer hyper-ellipsoids than hyper-spheres are needed to achieve similar coverage of nonself space in a negative selection problem. Experimentation validates this conjecture. In pedagogical benchmark problems, the number of hyper-ellipsoids to achieve good results is significantly (~50%) smaller than the associated number of hyper-spheres.
7th Annual Conference on Genetic and Evolutionary Computation
Shapiro, J. M., Lamont, G. B., & Peterson, G. L. (2005). An evolutionary algorithm to generate hyper-ellipsoid detectors for negative selection. Proceedings of the 7th Annual Conference on Genetic and Evolutionary Computation, 337–344. https://doi.org/10.1145/1068009.1068063