Solving of optimization and identification problems by the committee methods

摘要

A p-committee (where 0 ⩽ p < 1) for a system of sets {Mj:jϵJ} is such a finite set K that |K∩Mj|>p|K|(∀jϵJ).The paper discusses theorems of existence of p-committees for an arbitrary finite system of sets and for the finite system of half-spaces.The definition of a p-committee of functions discriminating sets in the space Rn is introduced. The existence theorem for a discriminating committee, consisting of affine functions which are to be used in the solution of problems of pattern recognition, is presented. Evaluation of the number of minimal committee members is given, also algorithms for plotting the committees (including the minimal). The paper discusses some applications of the committee technique in regard to economics, sociology, biology and medicine. Software data are reported as well.