On Fast Computation of Gradients for CANDECOMP/PARAFAC Algorithms

Abstract

Product between mode-$n$ unfolding $\bY_{(n)}$ of an $N$-D tensor $\tY$ and Khatri-Rao products of $(N-1)$ factor matrices $\bA^{(m)}$, $m=1,...,n-1,n+1,...,N$ exists in algorithms for CANDECOMP/PARAFAC (CP). If $\tY$ is an error tensor of a tensor approximation, this product is the gradient of a cost function with respect to factors, and has the largest workload in most CP algorithms. In this paper, a fast method to compute this product is proposed. Experimental verification shows that the fast CP gradient can accelerate the CP_ALS algorithm 2 times and 8 times faster for factorizations of 3-D and 4-D tensors, and the speed-up ratios can be 20-30 times for higher dimensional tensors.

12 pages, 2 figures

References in corpus (1)

• Low Complexity Damped Gauss-Newton Algorithms for CANDECOMP/PARAFAC

Cited by in corpus (2)

• CANDECOMP/PARAFAC Decomposition of High-order Tensors Through Tensor Reshaping
• Efficient Nonnegative Tensor Factorization via Saturating Coordinate Descent