PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Tensor ranks and some properties of tensor spaces
Pierre Comon
In: 2nd Workshop on Tensor Decompositions and Applications, 29 Aug - 02 Sept 2005, Luminiy, France.

Abstract

The Singular Value Decomposition (SVD) may be extended to tensors at least in two very different ways. One is the High-Order SVD, and the other is the Canonical Decomposition (CanD). Only the latter is closely related to the Tensor Rank. Important basic questions can be raised, such as the maximal achievable rank of a tensor of given dimensions, or the computation of a CanD. Some questions are answered, and it turns out that the answers depend on the choice of the underlying field, and on tensor symmetry structure, which outlines major differences compared to matrices.

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EPrint Type:Conference or Workshop Item (Tutorial)
Additional Information:Slides of the Tutorial
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:1638
Deposited By:Pierre Comon
Deposited On:28 November 2005