Doubly robust logistic regression for image classification

Abstract

The growing prevalence of image data in engineering and medical applications motivates the need for classification performance that are robust against outliers. To facilitate efficient and data-driven classification and recovery method, in this paper, we propose a novel supervised learning strategy based on the robust principal component analysis for third-order tensor and minimum distance criterion L2E for logistic regression, which is named as doubly robust logistic regression. Our work applies the ADMM method to obtain updating algorithm, and its global convergence is established even though L2E loss function is non-convex. We also extend the estimation procedure to the case of incomplete observation in input matrix. The numerical experiments demonstrate the advantages of combining the logistic L2E with tensor robust principal component analysis which can not only increase the accuracy of classification but also improve the recovery accuracy of noisy image. Three real data analysis are further used to examine the outperformance of our proposed method over the stat-of-art.