Non-negative Tensor Factorization With Applications To Statistics And Computer Vision

Abstract

We derive algorithms for finding a non-negative <i>n</i>-dimensional tensor factorization (<i>n</i>-NTF) which includes the non-negative matrix factorization (NMF) as a particular case when <i>n</i> = 2. We motivate the use of <i>n</i>-NTF in three areas of data analysis: (i) connection to latent class models in statistics, (ii) sparse image coding in computer vision, and (iii) model selection problems. We derive a "direct" positive-preserving gradient descent algorithm and an alternating scheme based on repeated multiple rank-1 problems.