Efficient Nonnegative Matrix Factorization via projected Newton method

Authors:
Pinghua Gong;Changshui Zhang
Affiliations:
State Key Laboratory on Intelligent Technology and Systems, Tsinghua National Laboratory for Information Science and Technology (TNList), Department of Automation, Tsinghua University, Beijing 100 ...;State Key Laboratory on Intelligent Technology and Systems, Tsinghua National Laboratory for Information Science and Technology (TNList), Department of Automation, Tsinghua University, Beijing 100 ...
Venue:
Pattern Recognition
Year:
2012

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Abstract

Nonnegative Matrix Factorization (NMF) is a popular decomposition technique in pattern analysis, document clustering, image processing and related fields. In this paper, we propose a fast NMF algorithm via Projected Newton Method (PNM). First, we propose PNM to efficiently solve a nonnegative least squares problem, which achieves a quadratic convergence rate under appropriate assumptions. Second, in the framework of an alternating optimization method, we adopt PNM as an essential subroutine to efficiently solve the NMF problem. Moreover, by exploiting the low rank assumption of NMF, we make PNM very suitable for solving NMF efficiently. Empirical studies on both synthetic and real-world (text and image) data demonstrate that PNM is quite efficient to solve NMF compared with several state of the art algorithms.