Support matrix machine with truncated pinball loss for classification

Abstract

With the expansion of vector-based classifiers to matrix-based classifiers, noise insensitivity and sparsity have always been the focal points. Existing SMM and Pin-SMM enjoy the former and the latter separately. To remedy the shortcoming, we propose a support matrix machine based on truncated pinball loss (TPin-SMM) in this paper, which integrates noise insensitivity and sparsity simultaneously. Thanks to the adding of two quantiles, it possesses precious properties including Bayes rule and bounding misclassification error as well. Concerning the non-convexity of TPin-SMM, a targeted CCCP-ADMM algorithm is established, which decomposes the problem into three sub-problems of each sub-iteration. To verify the validity of TPin-SMM, we have conducted numerical experiments on image datasets, EEG signal sets and Daimler Pedestrian Classification Benchmark dataset with different noises, all of them pass the statistical tests.