CP decomposition and weighted clique problem

CP decomposition and weighted clique problem

The determination of the optimal subdecomposition based on CP decomposition for high-order tensors is not straightforward because the rank-one tensors are not orthogonal. We show that this is equivalent to the weighted clique problem. Thus, it is NP-hard.

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Bibliographic Details
Published in:Statistics & probability letters Vol. 161; p. 108723
Main Author: Zhang, Tonglin
Format: Journal Article
Language:English
Published: Elsevier B.V 01-06-2020
Subjects:
CP decomposition
Dimension reduction
NP-hard
Subdecomposition
Tensors
Weighted clique problem
Dimension reduction
62M45
NP-hard
Tensors
Subdecomposition
CP decomposition
Weighted clique problem
62H25
Online Access:Get full text
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Description
Summary:The determination of the optimal subdecomposition based on CP decomposition for high-order tensors is not straightforward because the rank-one tensors are not orthogonal. We show that this is equivalent to the weighted clique problem. Thus, it is NP-hard.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2020.108723