Robust nonnegative matrix factorization using L21-norm

Authors:
Deguang Kong;Chris Ding;Heng Huang
Affiliations:
University of Texas at Arlington, Arlington, USA;University of Texas at Arlington, Arlington, USA;Dept. of Computer Science and Engineering, Arlington, USA
Venue:
Proceedings of the 20th ACM international conference on Information and knowledge management
Year:
2011

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Abstract

Nonnegative matrix factorization (NMF) is widely used in data mining and machine learning fields. However, many data contain noises and outliers. Thus a robust version of NMF is needed. In this paper, we propose a robust formulation of NMF using L21 norm loss function. We also derive a computational algorithm with rigorous convergence analysis. Our robust NMF approach, (1) can handle noises and outliers; (2) provides very efficient and elegant updating rules; (3) incurs almost the same computational cost as standard NMF, thus potentially to be used in more real world application tasks. Experiments on 10 datasets show that the robust NMF provides more faithful basis factors and consistently better clustering results as compared to standard NMF.