Parallel nonnegative tensor factorization via newton iteration on matrices

Abstract

Nonnegative Matrix Factorization (NMF) is a technique to approximate a large nonnegative matrix as a product of two significantly smaller nonnegative matrices. Since matrices can be seen as second-order tensors, NMF can be generalized to Nonnegative Tensor Factorization (NTF). To compute an NTF, the tensor problem can be transformed into a matrix problem by using matricization. Any NMF algorithm can be used to process such a matricized tensor, including a method based on Newton iteration. Here, an approach will be presented to adopt our parallel design of the Newton algorithm for NMF to compute an NTF in parallel for tensors of any order.