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A Multilinear Singular Value Decomposition
TLDR
We discuss a multilinear generalization of the singular value decomposition. Expand
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  • 489
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On the Best Rank-1 and Rank-(R1 , R2, ... , RN) Approximation of Higher-Order Tensors
TLDR
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. Expand
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Signal Processing based on Multilinear Algebra
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Tensor Decomposition for Signal Processing and Machine Learning
TLDR
This overview article aims to provide a good starting point for researchers and practitioners interested in learning about and working with tensors. Expand
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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
In this paper we introduce a new class of tensor decompositions. Intuitively, we decompose a given tensor block into blocks of smaller size, where the size is characterized by a set of mode-$n$Expand
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Fourth-Order Cumulant-Based Blind Identification of Underdetermined Mixtures
TLDR
In this paper we study two fourth-order cumulant-based techniques for the estimation of the mixing matrix in underdetermined independent component analysis. Expand
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A Link between the Canonical Decomposition in Multilinear Algebra and Simultaneous Matrix Diagonalization
  • L. Lathauwer
  • Mathematics, Computer Science
  • SIAM J. Matrix Anal. Appl.
  • 1 August 2006
TLDR
We derive a new and relatively weak deterministic sufficient condition for uniqueness of higher-order tensors which have the property that the rank is smaller than the greatest dimension. Expand
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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 leastsquaresExpand
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Fetal electrocardiogram extraction by blind source subspace separation
TLDR
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 multilead cutaneous potential recordings. Expand
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Blind Identification of Underdetermined Mixtures by Simultaneous Matrix Diagonalization
TLDR
We study simultaneous matrix diagonalization-based techniques for the estimation of the mixing matrix in underdetermined independent component analysis (ICA). Expand
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