Non-negative tensor factorization with applications to statistics and computer vision

We derive algorithms for finding a nonnegative n-dimensional tensor factorization (n-NTF) which includes the non-negative matrix factorization (NMF) as a particular case when n = 2. We motivate the use of n-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.

• Type: Conference
• Year: 2005
• Where: ICML
• Authors: Amnon Shashua, Tamir Hazan
• Keywords: Gradient Descent Algorithm, ICML 2005, Machine Learning, N-dimensional Tensor Factorization, Non-Negative Matrix Factorization