Solving non-negative matrix factorization by alternating least squares with a modified strategy

Authors:
Hongwei Liu;Xiangli Li;Xiuyun Zheng
Affiliations:
Department of Mathematics, Xidian University, Xi'an, People's Republic of China 710071;Department of Mathematics, Xidian University, Xi'an, People's Republic of China 710071 and College of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, People' ...;Department of Mathematics, Xidian University, Xi'an, People's Republic of China 710071
Venue:
Data Mining and Knowledge Discovery
Year:
2013

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Abstract

Non-negative matrix factorization (NMF) is a method to obtain a representation of data using non-negativity constraints. A popular approach is alternating non-negative least squares (ANLS). As is well known, if the sequence generated by ANLS has at least one limit point, then the limit point is a stationary point of NMF. However, no evdience has shown that the sequence generated by ANLS has at least one limit point. In order to overcome this shortcoming, we propose a modified strategy for ANLS in this paper. The modified strategy can ensure the sequence generated by ANLS has at least one limit point, and this limit point is a stationary point of NMF. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.