CANDECOMP/PARAFAC Decomposition of High-Order Tensors Through Tensor Reshaping

By Anh Huy Phan, Petr Tichavský, Andrzej S. Cichocki. 2012

62 citations recorded by the source corpus.

In general, algorithms for order-3 CANDECOMP/ PARAFAC (CP), also coined canonical polyadic decomposition (CPD), are easy to implement and can be extended to higher order CPD. Unfortunately, the algorithms become computationally demanding, and they are often not applicable to higher order and relatively large scale tensors. In this paper, by exploiting the uniqueness of CPD and the relation of a tensor in Kruskal form and its unfolded tensor, we propose a fast approach to deal with this problem. Instead of directly factorizing the high order data tensor, the method decomposes an unfolded tensor with lower order, e.g., order-3 tensor. On the basis of the order-3 estimated tensor, a structured Kruskal tensor, of the same dimension as the data tensor, is then generated, and decomposed to find the final solution using fast algorithms for the structured CPD. In addition, strategies to unfold tensors are suggested and practically verified in the paper.

Subfields: Computational Mathematics, Electrical and Electronic Engineering

Citations in the corpus

• Tensors : A brief introduction (2014, unknown): “In a similar spirit, for low-rank tensors of order larger than 3, one can also decrease the order by working jointly on tensor slices of lower orders [29], or by rearranging the original tensor into another of lower order but larger dimensions [64].”