A Fast Algorithm for Nonnegative Tensor Factorization using Block Coordinate Descent and an Active-set-type method

Nonnegative factorization of tensors plays an important role in the analysis of multi-dimensional data in which each element is inherently nonnegative. It provides a meaningful lower rank approximation, which can further be used for dimensionality reduction, data compression, text mining, or visualization. In this paper, we propose a fast algorithm for nonnegative tensor factorization (NTF) based on the alternating nonnegative least squares framework. To efficiently solve the nonnegativity-constrained least squares problems, we adopted a block principal pivoting algorithm that included additional improvements exploiting the common characteristics of NTF computation. The effectiveness and efficiency of the proposed algorithm are demonstrated through experiments using various real-world and synthetic data sets. We observed that the proposed algorithm significantly outperformed existing ones in computational speed.