The Method of Virtual Experts in Mathematical Diagnostics

Mathematical Diagnostics (MD) deals with identification problems arising in different practical areas. Some of these problems can be described by mathematical models where it is required to identify points belonging to two or more sets of points. Most of the existing tools provide some identification rule (a classifier) by means of which a given point is assigned (attributed) to one of the given sets. Each classifier can be viewed as a virtual expert. If there exist several classifiers (experts), the problem of evaluation of experts’ conclusions arises. In the paper for the case of supervised classification the method of virtual experts (the VE-method) is described. Based on this method, a generalized VE method is proposed where each of the classifiers can be chosen from a given family of classifiers. As a result, a new optimization problem with a discontinuous functional is stated. Examples illustrating the proposed approach are provided. The work of the second author was supported by the Russian Foundation for Fundamental Studies (RFFI) under Grant No 03-01-00668.