On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors

Authors:
Lieven De Lathauwer;Bart De Moor;Joos Vandewalle
Affiliations:
-;-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2000

Citing 0
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Abstract

In this paper we discuss a multilinear generalization of the best rank-R approximation problem for matrices, namely, the approximation of a given higher-order tensor, in an optimal least-squares sense, by a tensor that has prespecified column rank value, row rank value, etc. For matrices, the solution is conceptually obtained by truncation of the singular value decomposition (SVD); however, this approach does not have a straightforward multilinear counterpart. We discuss higher-order generalizations of the power method and the orthogonal iteration method.