Non-Negative Matrix Factorization as a Feature Selection Tool for Maximum Margin Classifiers

Mithun Das Gupta, Jing Xiao

Abstract: Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition tool for multivariate data. Non-negative bases allow strictly additive combinations which have been shown to be part-based as well as relatively sparse. We pursue a discriminative decomposition by coupling NMF objective with a maximum margin classifier, specifically a support vector machine (SVM). Conversely, we propose an NMF based regularizer for SVM. We formulate the joint update equations and propose a new method which identifies the decomposition as well as the classification parameters. We present classification results on synthetic as well as real datasets.