Fast Nonnegative Tensor Factorization with an Active-Set-Like Method

We introduce an efficient algorithm for computing a low-rank nonnegative CANDECOMP/PARAFAC (NNCP) decomposition. In text mining, signal processing, and computer vision among other areas, imposing nonnegativity constraints to low-rank factors has been shown an effective technique providing physically meaningful interpretation. A principled methodology for computing NNCP is alternating nonnegative least squares, in which nonnegativity-constrained least squares (NNLS) problems are solved in each iteration. In this chapter, we propose to solve the NNLS problems using the block principal pivoting method. The block principal pivoting method overcomes some difficulties of the classical active method for NNLS problems with large variables. We introduce techniques to accelerate the block principal pivoting method for multiple right-hand sides, which is typical in NNCP computation. Computational experiments show the state-of-the-art performance of the proposed method.