Variable Selection for Efficient Nonnegative Tensor Factorization

Nonnegative Tensor Factorization (NTF) has become a popular tool for extracting informative patterns from tensor data. However, NTF has high computational cost both in space and in time, mostly in iterative calculation of the gradient. In this paper, we consider variable selection to reduce the cost, assuming sparsity of the factor matrices. In fact, it is known that the factor matrices are often very sparse in many applications such as network analysis, text analysis and image analysis. We update only a small subset of important variables in each iterative step. We show the effectiveness of the algorithm analytically and experimentally in comparison with conventional NTF algorithms. The algorithm was five times faster than the naive algorithm in the best case and required one to five hundred times less memory while keeping the approximation accuracy as the same.