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arXiv · 1204.1586

On Fast Computation of Gradients for CANDECOMP/PARAFAC Algorithms

Anh Huy Phan·Petr Tichavský·Andrzej Cichocki
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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.

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Anh Huy Phan, Petr Tichavský, Andrzej Cichocki. 2012-04-07. On Fast Computation of Gradients for CANDECOMP/PARAFAC Algorithms. https://arxiv.org/abs/1204.1586

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