Correlation classifiers based on data perturbation: New formulations and algorithms

摘要

This paper develops a novel framework for a family of correlation classifiers that are reconstructed from uncertain convex programs under data perturbation. Under this framework, correlation classifiers are exploited from the pessimistic viewpoint under possible perturbation of data, and the max-min optimization problem is formulated by simplifying the original model in terms of adaptive uncertainty regions. The proposed model can be formulated as a minimization problem under proper conditions. The proximal majorization-minimization optimization (PMMO) based on Bregman divergences is devised to solve the proposed model that may be nonconvex or nonsmooth. It is found that using PMMO to solve the proposed model can exploit the convergence rate of the solution sequence in the nonconvex case. In the case of specific functions we can use the accelerated versions of first-order methods to solve the proposed model with convexity in order to make them have fast convergence rates in terms of the objective function. Extensive experiments on some data sets are conducted to demonstrate the feasibility and validity of the proposed model. (C) 2019 Elsevier Ltd. All rights reserved.