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Blind identification of overcomplete mixtures of sources
 BIOME)”, Lin. Algebra Appl
, 2004
"... The problem of Blind Identification of linear mixtures of independent random processes is known to be related to the diagonalization of some tensors. This problem is posed here in terms of a non conventional joint approximate diagonalization of several matrices. In fact, a congruent transform is app ..."
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Cited by 14 (11 self)
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The problem of Blind Identification of linear mixtures of independent random processes is known to be related to the diagonalization of some tensors. This problem is posed here in terms of a non conventional joint approximate diagonalization of several matrices. In fact, a congruent transform is applied to each of these matrices, the left transform being rectangular full rank, and the right one being unitary. The application in antenna signal processing is described, and suboptimal numerical algorithms are proposed.
SYMMETRIC TENSOR DECOMPOSITION
, 2009
"... We present an algorithm for decomposing a symmetric tensor of dimension n and order d as a sum of of rank1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for symmetric tensors of dimension 2. We exploit the known fact that every symmetric tensor is equivalently represented ..."
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Cited by 13 (4 self)
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We present an algorithm for decomposing a symmetric tensor of dimension n and order d as a sum of of rank1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for symmetric tensors of dimension 2. We exploit the known fact that every symmetric tensor is equivalently represented by a homogeneous polynomial in n variables of total degree d. Thus the decomposition corresponds to a sum of powers of linear forms. The impact of this contribution is twofold. First it permits an efficient computation of the decomposition of any tensor of subgeneric rank, as opposed to widely used iterative algorithms with unproved convergence (e.g. Alternate Least Squares or gradient descents). Second, it gives tools for understanding uniqueness conditions, and for detecting the tensor rank.
Computing symmetric rank for symmetric tensors
 J. SYMBOLIC COMPUT
, 2011
"... We consider the problem of determining the symmetric tensor rank for symmetric tensors with an algebraic geometry approach. We give algorithms for computing the symmetric rank for 2 × · · · × 2 tensors and for tensors of small border rank. From a geometric point of view, we describe the symmetri ..."
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Cited by 12 (4 self)
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We consider the problem of determining the symmetric tensor rank for symmetric tensors with an algebraic geometry approach. We give algorithms for computing the symmetric rank for 2 × · · · × 2 tensors and for tensors of small border rank. From a geometric point of view, we describe the symmetric rank strata for some secant varieties of Veronese varieties.
Multihomogeneous polynomial decomposition using moment matrices
 International Symposium on Symbolic and Algebraic Computation
, 2011
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 4 (3 self)
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
GENERAL TENSOR DECOMPOSITION, MOMENT MATRICES AND APPLICATIONS
, 2011
"... The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated moment matrix problem and give a new criterion for flat exten ..."
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Cited by 1 (1 self)
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The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated moment matrix problem and give a new criterion for flat extension of QuasiHankel matrices. We connect this criterion to the commutation characterisation of border bases. A new algorithm is described. It applies for general multihomogeneous tensors, extending the approach of J.J. Sylvester to binary forms. An example illustrates the algebraic operations involved in this approach and how the decomposition can be recovered from eigenvector computation.
École doctorale MSTIC Mathématiques et Sciences et Techniques de l’Information et de la Communication Thèse de doctorat
"... Étude des systèmes MIMO pour émetteurs monoporteuses dans le contexte de canaux sélectifs en fréquence Analysis of MIMO systems for singlecarrier transmitters in frequencyselective channels Soutenue le 16 décembre 2011 devant les membres du jury: ..."
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Étude des systèmes MIMO pour émetteurs monoporteuses dans le contexte de canaux sélectifs en fréquence Analysis of MIMO systems for singlecarrier transmitters in frequencyselective channels Soutenue le 16 décembre 2011 devant les membres du jury:
HIGHER SECANT VARIETIES OF Pn × Pm EMBEDDED IN BIDEGREE (1, d)
, 2011
"... Let X (n,m) (1,d) denote the SegreVeronese embedding of Pn × Pm via the sections of the sheaf O(1, d). We study the dimensions of higher secant varieties of X (n,m) (1,d) and we prove that there is no defective sth secant variety, except possibly for n values of s. Moreover when ( m+d) is a multip ..."
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Let X (n,m) (1,d) denote the SegreVeronese embedding of Pn × Pm via the sections of the sheaf O(1, d). We study the dimensions of higher secant varieties of X (n,m) (1,d) and we prove that there is no defective sth secant variety, except possibly for n values of s. Moreover when ( m+d) is a multiple of d (m + n + 1), the sth secant variety of X (n,m) has the expected dimension for (1,d) every s.
HAL author manuscript IEEE Signal Processing Magazine 2008;25(1):5768 HAL author manuscript inserm00202706, version 1
"... This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's co ..."
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This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. 1 ICA: a potential tool for BCI systems