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CANDECOMP/PARAFAC Decomposition of High-Order Tensors Through Tensor Reshaping
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SYSNO ASEP 0396775 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title CANDECOMP/PARAFAC Decomposition of High-Order Tensors Through Tensor Reshaping Author(s) Phan, A. H. (JP)
Tichavský, Petr (UTIA-B) RID, ORCID
Cichocki, A. (JP)Number of authors 3 Source Title IEEE Transactions on Signal Processing - ISSN 1053-587X
Roč. 61, č. 19 (2013), s. 4847-4860Number of pages 14 s. Publication form Print - P Language eng - English Country US - United States Keywords tensor factorization ; canonical polyadic decomposition ; Cramer-Rao bound Subject RIV BB - Applied Statistics, Operational Research R&D Projects GA102/09/1278 GA ČR - Czech Science Foundation (CSF) Institutional support UTIA-B - RVO:67985556 UT WOS 000324342900017 DOI 10.1109/TSP.2013.2269046 Annotation 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. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2014
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