Non-Negative Tensor Factorization: Refurbishing an Old Standby

• Activity Number: 587
• Type: Invited
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Eric C Chi*+ and Tamara G Kolda
• Companies: University of California at Los Angeles and Sandia National Laboratories
• Keywords: Nonnegative Tensor Factorization ; Multiplicative Updates ; Block Coordinate Descent

Abstract

Tensors have found application in a variety of fields from signal processing to bioinformatics and neuroimaging. In the latter two examples, data is nonnegative and estimating nonnegative multilinear models can yield more interpretable physical model by representing the data as a sum of nonnegative components. Algorithms for estimating such models abound, and counted among the throng are tensor extensions of the popular multiplicative Lee-Seung (LS) nonnegative matrix factorization algorithm. LS algorithms remain popular due to their simplicity. Yet is is well known that they can converge to non-stationary points. Instead of resolving the convergence issue, however, efforts have focused on developing faster algorithms with alternative strategies for which convergence can be proven. Nonetheless in practice LS algorithms are competitive with respect to wall-clock speed. Because of their simplicity and performance, the convergence issues of the LS approach warrant further investigation. We introduce a block-coordinate descent nonnegative tensor factorization algorithm for which the LS algorithm is a special case. Our algorithm converges to KKT points under mild conditions.