Mathematical diagnostics via nonsmooth analysis

Abstract

Mathematical Diagnostics (MD) deals with identification problems arising in different practical areas. In the paper, the problem of the choice of a classifier and a functional is discussed. Existing methods of linear discriminant analysis are based on linear and quadratic programming. The usage of nonlinear and even nonsmooth criteria and classifiers may improve the quality of identification. Successful application of nonsmooth discriminant analysis is possible if proper nonsmooth software is taylored for specific problems of MD.

Keywords:

• Identification
• Separation
• Mathematical diagnostics
• Nonsmooth analysis
• Nondifferentiable optimization
• Linear discriminant analysis
• Nonsmooth discriminant analysis
• Clustering

Acknowledgements

The author became involved in diagnostics problems under the influence of A.M. Rubinov and M. Gaudioso who, from different directions, attacked these problems by tools of nonsmooth analysis. Thanks are also due to V. Roschina and the anonymous referees for their useful remarks and suggestions. The work was supported by the Russian Foundation for Fundamental Studies (RFFI) under Grant No. 03-01-00668.