Toward Faster Nonnegative Matrix Factorization: A New Algorithm and Comparisons

Nonnegative Matrix Factorization (NMF) is a dimension reduction method that has been widely used for various tasks including text mining, pattern analysis, clustering, and cancer class discovery. The mathematical formulation for NMF appears as a non-convex optimization problem, and various types of algorithms have been devised to solve the problem. The alternating nonnegative least squares (ANLS) framework is a block coordinate descent approach for solving NMF, which was recently shown to be theoretically sound and empirically efficient. In this paper, we present a novel algorithm for NMF based on the ANLS framework. Our new algorithm builds upon the block principal pivoting method for the nonnegativity constrained least squares problem that overcomes some limitations of active set methods. We introduce ideas to efficiently extend the block principal pivoting method within the context of NMF computation. Our algorithm inherits the convergence theory of the ANLS framework and can eas...

• Type: Conference
• Year: 2008
• Where: ICDM
• Authors: Jingu Kim, Haesun Park
• Keywords: Algorithm, Block Principal Pivoting, Data Mining, ICDM 2008, Principal Pivoting Method