Non-Negative Matrix Factorization: Estimation of the Number of Components and the Effect of Normalization

• Activity Number: 383
• Type: Contributed
• Date/Time: Tuesday, August 4, 2009 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Jose Maisog*+ and Karthik Devarajan and S. Stanley Young and Paul Fogel and George Luta
• Companies: Georgetown University and Fox Chase Cancer Center and National Institute of Statistical Sciences and Independent Consultant and Georgetown University
• Keywords: non-negative matrix factorization ; decomposition ; components ; dimensionality reduction ; normalization ; simulations

Abstract

Non-negative matrix factorization (NMF; Lee and Seung, 1999) is a relatively new matrix factorization method, successfully utilized in many recent applications in Computational Biology. NMF factors an N-by-M non-negative data matrix into an N-by-k matrix and a k-by-M matrix. To assess the important issue of identifying the number of components k, the performance of several methods for estimating k (including Minka, 2000; Fogel et al., 2008; Zhu and Ghodsi, 2006) was evaluated on simulated data with a known number of components, as well as on a well-known data set (Golub et al., 1999). To assess the effect of normalization, various proposed methods (Pascual-Montano et al., 2006) were applied prior to the factorization. The simulation results provide preliminary guidelines for the practical use of NMF.