Finding the Largest Hypercavity in a Linear Data Space

This paper proposes a definition and a solution of the problem of finding a hyper cavity as a data-free hyper sphere of maximum radius. This problem is formulated here as a multiextremal problem under constraints in a linear feature space and in a linear space produced by a kernel function. In accordance with the proposed approach, just as in the one-class SVM, the center of the hyper sphere is sought for as a linear combination of some small quantity of so called "support" objects. Experiments with smulated points in a 2-dimensional feature space and with symbolic sequences modeling a global evolutionary process have demonstrated correctness of the obtained solution.