PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Generic and Typical Ranks of Three-Way Arrays
Pierre Comon and Jos ten Berge
(2006) Project Report. I3S, Sophia-Antipiolis, France.

Abstract

The concept of tensor rank, introduced in the twenties, has been popularized at the beginning of the seventies. This has allowed to carry out Factor Analysis on arrays with more than two indices. The generic rank may be seen as an upper bound to the number of factors that can be extracted from a given tensor. We explain in this short paper how to obtain numerically the generic rank of tensors of arbitrary dimensions, and compare it with the rare algebraic results already known at order three. In particular, we examine the cases of symmetric tensors, tensors with symmetric matrix slices, or tensors with free entries.

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EPrint Type:Monograph (Project Report)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Theory & Algorithms
ID Code:2325
Deposited By:Pierre Comon
Deposited On:22 November 2006