JHPCS 2016: High-Performance Scientific Computing

Abstract

We introduce an efficient algorithm for computing a low-rank non- negative CANDECOMP/PARAFAC (NNCP) decomposition. In textmining, signal processing, and computer vision among other areas, imposing nonneg- ativity constraints to the low-rank factors of matrices and tensors has been shown an effective technique providing physically meaningful interpretation. A principled methodology for computing NNCP is alternating nonnegative least squares, in which the 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 the NNLS problems with a large number of variables. We intro- duce techniques to accelerate the block principal pivotingmethod formultiple right-hand sides, which is typical in NNCP computation. Computational ex- periments