Decision Rule Robustness under Distortions of Observations to be Classified

Abstract

This chapter is devoted to problems of robust pattern recognition for common in practice types of distortions of multivariate observations subject to classification: Tukey-Huber type contaminations, additive distortions of observations (including round-off errors), distortions produced by mixtures of probability distributions, distortions defined by means of L ₂-metric, or χ ²-metric, or variation metric, and random distortions of probability distributions. Using the asymptotic expansion method, we find estimates for the robustness factor and critical distortion levels (“breakdown points”). We also construct robust decision rules that minimize the guaranteed risk value.