Robust Multinomial Logistic Regression Based on RPCA

Multiclass classification tasks are ubiquitous recently. In this scenario, the class label usually takes more than two possible discrete outcomes. As a simple and successful model, the multinomial logistic regression, also known as the softmax regression, is widely used in many multiclass classification applications. However, the existing method often experiences significant performance degradation when gross outliers are present in data features. To this end, in this paper, a novel robust multinomial logistic regression method is proposed by solving a rank minimization problem. In particular, the recovery of clean data and the logistic regression learning are conducted jointly. As such, the detection of the intra-sample outliers within data, by robust principal component analysis, is performed in a supervised way. Although the problem is nonconvex and nonsmooth, the convergence is guaranteed by the recent theoretical advance of alternating direction method of multipliers. Experimental analysis on synthetic and real-world data demonstrates that our method outperforms other state-of-the-art ones, in terms of classification accuracy.