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A Multilinear Singular Value Decomposition
TLDR
There is a strong analogy between several properties of the matrix and the higher-order tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, first-order perturbation effects, etc., are analyzed.
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On the Best Rank-1 and Rank-(R1 , R2, ... , RN) Approximation of Higher-Order Tensors
TLDR
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, rowRank value, etc.
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Tensor Decomposition for Signal Processing and Machine Learning
TLDR
The material covered includes tensor rank and rank decomposition; basic tensor factorization models and their relationships and properties; broad coverage of algorithms ranging from alternating optimization to stochastic gradient; statistical performance analysis; and applications ranging from source separation to collaborative filtering, mixture and topic modeling, classification, and multilinear subspace learning.
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Signal Processing based on Multilinear Algebra
Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis
TLDR
Benefiting from the power of multilinear algebra as their mathematical backbone, data analysis techniques using tensor decompositions are shown to have great flexibility in the choice of constraints which match data properties and extract more general latent components in the data than matrix-based methods.
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Decompositions of a Higher-Order Tensor in Block Terms - Part II: Definitions and Uniqueness
  • L. Lathauwer
  • Mathematics, Computer Science
    SIAM J. Matrix Anal. Appl.
  • 1 September 2008
TLDR
A new class of tensor decompositions is introduced, where the size is characterized by a set of mode-$n$ ranks, and conditions under which essential uniqueness is guaranteed are derived.
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Fourth-Order Cumulant-Based Blind Identification of Underdetermined Mixtures
TLDR
Two fourth-order cumulant-based techniques for the estimation of the mixing matrix in underdetermined independent component analysis based on a simultaneous matrix diagonalization and a simultaneous off-diagonalization are studied.
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A Link between the Canonical Decomposition in Multilinear Algebra and Simultaneous Matrix Diagonalization
  • L. Lathauwer
  • Mathematics
    SIAM J. Matrix Anal. Appl.
  • 1 August 2006
TLDR
This paper derives a new and relatively weak deterministic sufficient condition for uniqueness in the decomposition of higher-order tensors which have the property that the rank is smaller than the greatest dimension.
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Fetal electrocardiogram extraction by blind source subspace separation
We propose the emerging technique of independent component analysis, also known as blind source separation, as an interesting tool for the extraction of the antepartum fetal electrocardiogram from…
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On the Best Rank-1 and Rank-(
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 leastsquares…
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