Fast Projection-Based Methods for the Least Squares Nonnegative Matrix Approximation Problem

: Nonnegative matrix approximation (NNMA) is a popular matrix decomposition technique that has proven to be useful across a diverse variety of fields with applications ranging from document analysis and image processing to bioinformatics and signal processing. Over the years, several algorithms for NNMA have been proposed, e.g. Lee and Seung's multiplicative updates, alternating least squares (ALS), and gradient descent-based procedures. However, most of these procedures suffer from either slow convergence, numerical instability, or at worst, serious theoretical drawbacks. In this paper, we develop a new and improved algorithmic framework for the least-squares NNMA problem, which is not only theoretically well-founded, but also overcomes many deficiencies of other methods. Our framework readily admits powerful optimization techniques and as concrete realizations we present implementations based on the Newton, BFGS and conjugate gradient methods. Our algorithms provide numerical re...

• Type: Journal
• Year: 2008
• Where: SADM
• Authors: Dongmin Kim, Suvrit Sra, Inderjit S. Dhillon
• Keywords: Improved Algorithmic Framework, Matrix Decomposition Technique, Nonnegative Matrix Approximation, SADM 2008