Blind identification of MISO-FIR channels (2010)
Fernandes, Carlos Estevao Rolim, Comon, Pierre, Favier, Gérard
In this paper, we address the problem of determining the order of MISO channels by means of a series of hypothesis tests based on scalar statistics. Using estimated 4th-order output cumulants, we...
Blind identification of MISO-FIR channels (2010)
Fernandes, Carlos Estevao Rolim, Comon, Pierre, Favier, Gérard
In this paper, we address the problem of determining the order of MISO channels by means of a series of hypothesis tests based on scalar statistics. Using estimated 4th-order output cumulants, we...
On the typical rank of real binary forms (2009)
Comon, Pierre, Ottaviani, Giorgio
We determine the rank of a general real binary form of degree d=4 and d=5. In the case d=5, the possible values of the rank of such general forms are 3,4,5. The existence of three typical ranks was...
Initialization Free Graph Based Clustering (2009)
Galluccio, Laurent, Michel, Olivier J. J., Comon, Pierre, Slezak, Eric, Hero, Alfred O.
This paper proposes an original approach to cluster multi-component data sets, including an estimation of the number of clusters. From the construction of a minimal spanning tree with Prim's...
Cumulant Matching for Independent Source Extraction (2009)
Ronald Phlypo, Vicente Zarzoso, Pierre Comon, Ignace Lemahieu
Abstract — In this work we show how one can make use of priors on signal statistics under the form of cumulant guesses to extract an independent source from an observed mixture. The advantage of...
Blind Separation of Instantaneous Mixtures of Dependent Sources (2009)
Abstract. This paper deals with the problem of Blind Source Separation. Contrary to the vast majority of works, we do not assume the statistical independence between the sources and explicitly...
Abstract — The problems of signal separation and signal extraction arise in a wide variety of applications in biomedical engineering and other areas. Under the source statistical independence...
Comparative speed analysis of FastICA (2009)
Abstract. FastICA is arguably one of the most widespread methods for independent component analysis. We focus on its deflation-based implementation, where the independent components are extracted one...
Function in Diffusion MRI ⋆ (2009)
Aurobrata Ghosh, Elias Tsigaridas, Maxime Descoteaux, Pierre Comon, Bernard Mourrain, Rachid Deriche, ...
A polynomial based approach to extract the maxima of an antipodally symmetric spherical function and its application to extract fiber
Extraction of atrial activity from the ECG by spectrally constrained kurtosis sign based (2009)
Ronald Phlypo, Vicente Zarzoso, Pierre Comon, Ignace Lemahieu
Abstract. This paper deals with the problem of estimating atrial activity during atrial fibrillation periods in the electrocardiogram (ECG). Since the signal of interest differs in kurtosis sign from...
Subtracting a best rank-1 approximation may increase tensor rank (2009)
Stegeman, Alwin, Comon, Pierre
It has been shown that a best rank-R approximation of an order-k tensor may not exist when R>1 and k>2. This poses a serious problem to data analysts using tensor decompositions. It has been observed...
Tensor Decompositions, State of the Art and Applications (2009)
In this paper, we present a partial survey of the tools borrowed from tensor algebra, which have been utilized recently in Statistics and Signal Processing. It is shown why the decompositions well...
Nonnegative approximations of nonnegative tensors (2009)
We study the decomposition of a nonnegative tensor into a minimal sum of outer product of nonnegative vectors and the associated parsimonious naive Bayes probabilistic model. We show that the...
ICAR: A Tool for Blind Source Separation Using Fourth-Order Statistics Only (2009)
Laurent Albera, Anne Ferréol, Pascal Chevalier, Pierre Comon, Senior Member
Abstract—The problem of blind separation of overdetermined mixtures of sources, that is, with fewer sources than (or as many sources as) sensors, is addressed in this paper. A new method, called...
Symmetric tensor decomposition (2009)
Brachat, Jerome, Comon, Pierre, Mourrain, Bernard, Tsigaridas, Elias
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We...
Symmetric tensor decomposition (2009)
Brachat, Jerome, Comon, Pierre, Mourrain, Bernard, Tsigaridas, Elias
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We...
Symmetric tensor decomposition (2009)
Brachat, Jerome, Comon, Pierre, Mourrain, Bernard, Tsigaridas, Elias
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We...
Performance limits of alphabet diversities for FIR SISO channel identification (2009)
Delmas, Jean-Pierre, Meurisse, Yann, Comon, Pierre
Finite Impulse Responses (FIR) of Single-Input Single-Output (SISO) channels can be blindly identified from second order statistics of transformed data, for instance when the channel is excited by...
Blind Paraunitary Equalization (2009)
Icart, Sylvie, Comon, Pierre, Rota, Ludwig
In this paper a blind MIMO space-time equalizer is described, dedicated to convolutive mixtures when observations have been pre-whitened. Filters preserving space-time whiteness are paraunitary; a...
Performance limits of alphabet diversities for FIR SISO channel identification (2009)
Delmas, Jean-Pierre, Meurisse, Yann, Comon, Pierre
Finite Impulse Responses (FIR) of Single-Input Single-Output (SISO) channels can be blindly identified from second order statistics of transformed data, for instance when the channel is excited by...
Blind Paraunitary Equalization (2009)
Icart, Sylvie, Comon, Pierre, Rota, Ludwig
In this paper a blind MIMO space-time equalizer is described, dedicated to convolutive mixtures when observations have been pre-whitened. Filters preserving space-time whiteness are paraunitary; a...
Symmetric tensor decomposition (2009)
Brachat, Jerome, Comon, Pierre, Mourrain, Bernard, Tsigaridas, Elias
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We...
Symmetric tensor decomposition (2009)
Brachat, Jerome, Comon, Pierre, Mourrain, Bernard, Tsigaridas, Elias
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We...
Combining multiple partitions created with a graph-based construction for data clustering (2009)
Galluccio, Laurent, Michel, Olivier, Comon, Pierre, Hero, Alfred O., Kliger, Mark
This paper focusses on a new clustering method called evidence accumulation clustering with dual rooted prim tree cuts (EAC-DC), based on the principle of cluster ensembles also known as ``combining...
Combining multiple partitions created with a graph-based construction for data clustering (2009)
Galluccio, Laurent, Michel, Olivier, Comon, Pierre, Hero, Alfred O., Kliger, Mark
This paper focusses on a new clustering method called evidence accumulation clustering with dual rooted prim tree cuts (EAC-DC), based on the principle of cluster ensembles also known as ``combining...
Nonnegative approximations of nonnegative tensors (2009)
We study the decomposition of a nonnegative tensor into a minimal sum of outer product of nonnegative vectors and the associated parsimonious naive Bayes probabilistic model. We show that the...
Tensor Decompositions, Alternating Least Squares and other Tales (2009)
Comon, Pierre, Luciani, Xavier
This work was originally motivated by a classification of tensors proposed by Richard Harshman. In particular, we focus on simple and multiple ``bottlenecks'', and on ``swamps''. Existing theoretical...
Generic and Typical Ranks of Multi-Way Arrays (2009)
Comon, Pierre, Ten Berge, Jos, De Lathauwer, Lieven, Castaing, Josephine
The concept of tensor rank was introduced in the twenties. In the seventies, when methods of Component Analysis on arrays with more than two indices became popular, tensor rank became a much studied...
Tensors versus Matrices, usefulness and unexpected properties (2009)
Since the nineties, tensors are increasingly used in Signal Processing and Data Analysis. There exist striking differences between tensors and matrices, some being advantages, and others raising...
Tensors versus Matrices, usefulness and unexpected properties (2009)
Since the nineties, tensors are increasingly used in Signal Processing and Data Analysis. There exist striking differences between tensors and matrices, some being advantages, and others raising...
Initialization Free Graph Based Clustering (2009)
Galluccio, Laurent, Michel, Olivier, Comon, Pierre, Slezak, Eric, Hero, Alfred O.
This paper proposes an original approach to cluster multi-component data sets, including an estimation of the number of clusters. From the construction of a minimal spanning tree with Prim's...
Initialization Free Graph Based Clustering (2009)
Galluccio, Laurent, Michel, Olivier, Comon, Pierre, Slezak, Eric, Hero, Alfred O.
This paper proposes an original approach to cluster multi-component data sets, including an estimation of the number of clusters. From the construction of a minimal spanning tree with Prim's...
Arbres de recouvrement minimaux duaux et application à la segmentation non supervisée (2009)
GALLUCCIO, Laurent, MICHEL, Olivier, COMON, Pierre
Cet article propose de nouvelles approches pour la classification non supervisée. Nous proposons d'exploiter les propriétés d'une nouvelle mesure de distance exploitant la construction d'arbres de...
Symmetric tensor decomposition (2009)
Brachat, Jerome, Comon, Pierre, Mourrain, Bernard, Tsigaridas, Elias P.
We present an algorithm for decomposing a symmetric tensor of dimension n and order d as a sum of of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for symmetric...
Luciani, Xavier, Comon, Pierre
In this work, we consider the problem of blind identification of underdetermined mixtures in a cyclostationary context relying on sixth-order statistics. We propose to exploit the cyclostationarity...
Arbres de recouvrement minimaux duaux et application a la segmentation non supervisee (2009)
Galluccio, Laurent, Michel, Olivier, Comon, Pierre
Cet article propose de nouvelles approches de segmentation non supervisée. Nous proposons d'exploiter les propriétés d'une nouvelle mesure de distance reposant sur la construction d'arbres de...
Symmetric tensor decomposition (2009)
Brachat, Jerome, Comon, Pierre, Mourrain, Bernard, Tsigaridas, Elias P.
We present an algorithm for decomposing a symmetric tensor of dimension n and order d as a sum of of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for symmetric...
Luciani, Xavier, Comon, Pierre
In this work, we consider the problem of blind identification of underdetermined mixtures in a cyclostationary context relying on sixth-order statistics. We propose to exploit the cyclostationarity...
Arbres de recouvrement minimaux duaux et application a la segmentation non supervisee (2009)
Galluccio, Laurent, Michel, Olivier, Comon, Pierre
Cet article propose de nouvelles approches de segmentation non supervisée. Nous proposons d'exploiter les propriétés d'une nouvelle mesure de distance reposant sur la construction d'arbres de...
One decade of biomedical problems using ICA: a full comparative study (2009)
Albera, Laurent, Kachenoura, Amar, Karfoul, Ahmad, Comon, Pierre, Senhadji, Lotfi
This communication aims at giving some insights into the use of Independent Component Analysis (ICA) for solving biomedical problems. First the concept of ICA is reviewed and different classes of ICA...
Subtracting a best rank-1 approximation may increase tensor rank (2009)
Stegeman, Alwin, Comon, Pierre
Is has been shown that a best rank-R approximation of an order-k tensor may not exist when R is at most 2 and k is at most 3. This poses a serious problem to data analysts using Candecomp/Parafac and...
Subtracting a best rank-1 approximation may increase tensor rank (2009)
Stegeman, Alwin, Comon, Pierre
Is has been shown that a best rank-R approximation of an order-k tensor may not exist when R is at most 2 and k is at most 3. This poses a serious problem to data analysts using Candecomp/Parafac and...
Comparative Speed Analysis of FastICA (2008)
Abstract. FastICA is arguably one of the most widespread methods for independent component analysis. We focus on its deflation-based implementation, where the independent components are extracted one...
ORDER DETECTION AND BLIND IDENTIFICATION OF 2 × 1 MISO CHANNELS (2008)
Carlos Estêvão, R. Fern, Pierre Comon, Gérard Favier
In this paper, we investigate the use of output 4th-order cumulants to detect the number of source signals on a multipleinput single-output (MISO) communications channel and blindly identify their...
Blind Separation of Discrete Sources Olivier GRELLIER Student Member, IEEE, (2008)
Abstract — A polynomial criterion is proposed to perform blind source separation, extending previous works to MIMO systems. The criterion is proved to be asymptotically MAP-equivalent in presence...
(OFDM) systems. We show that the received signal forms a 4-way tensor whose dimensions are space, time, and frequency, and can be written as a sum of tensor products (over paths and users) of four...
Pierre Comon, Gene Golub, Lek-heng Lim, Bernard Mourrain
Abstract. A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric...
Blind identification of underdetermined mixtures based on the hexacovariance (2008)
Laurent Albera, Pierre Comon, Pascal Chevalier, Anne Ferréol
Static linear mixtures with more sources than sensors are considered. Blind Identification (BI) of underdetermined mixtures is addressed by taking advantage of Sixth Order (SixO) statistics and the...
Structured matrices and inverses (2008)
A matrix (and any associated linear system) will be referred to as structured if it has a small displacement rank. It is known that the inverse of a structured matrix is structured, which allows fast...
Symmetric tensors and symmetric tensor rank (2008)
Comon, Pierre, Golub, Gene, Lim, Lek-Heng, Mourrain, Bernard
A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a sum of symmetric outer...
ICA: A Potential Tool for BCI Systems (2008)
Kachenoura, Amar, Albera, Laurent, Senhadji, Lotfi, Comon, Pierre
Several studies dealing with independent component analysis (ICA)-based brain-computer interface (BCI) systems have been reported. Most of them have only explored a limited number of ICA methods,...
ICA: A Potential Tool for BCI Systems (2008)
Kachenoura, Amar, Albera, Laurent, Senhadji, Lotfi, Comon, Pierre
Several studies dealing with independent component analysis (ICA)-based brain-computer interface (BCI) systems have been reported. Most of them have only explored a limited number of ICA methods,...
Optimal Step-Size Constant Modulus Algorithm (2008)
Zarzoso, Vicente, Comon, Pierre
The step size leading to the global minimum of the constant modulus (CM) criterion along the search direction can be obtained algebraically at each iteration among the roots of a third-degree...
Enhanced Line Search : A Novel Method to Accelerate PARAFAC (2008)
Rajih, Myriam, Comon, Pierre, Harshman, Richard
Several modifications have been proposed to speed up the Alternating Least Squares (ALS) method of fitting the Parafac model. The most widely used is Line Search, which extrapolates from linear...
Optimal Step-Size Constant Modulus Algorithm (2008)
Zarzoso, Vicente, Comon, Pierre
The step size leading to the global minimum of the constant modulus (CM) criterion along the search direction can be obtained algebraically at each iteration among the roots of a third-degree...
Generic and Typical Ranks of Three-Way Arrays (2008)
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...
Symmetric tensors and symmetric tensor rank (2008)
Comon, Pierre, Golub, Gene, Lim, Lek-Heng, Mourrain, Bernard
A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric sum of outer...
Generic and Typical Ranks of Three-Way Arrays (2008)
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...
Enhanced Line Search : A Novel Method to Accelerate PARAFAC (2008)
Rajih, Myriam, Comon, Pierre, Harshman, Richard
Several modifications have been proposed to speed up the Alternating Least Squares (ALS) method of fitting the Parafac model. The most widely used is Line Search, which extrapolates from linear...
Symmetric tensors and symmetric tensor rank (2008)
Comon, Pierre, Golub, Gene, Lim, Lek-Heng, Mourrain, Bernard
A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric sum of outer...
Zarzoso, Vicente, Comon, Pierre
The problems of signal separation and signal extraction arise in a wide variety of applications in biomedical engineering and other areas. Under the source statistical independence assumption, these...
Zarzoso, Vicente, Comon, Pierre
The problems of signal separation and signal extraction arise in a wide variety of applications in biomedical engineering and other areas. Under the source statistical independence assumption, these...
Galluccio, Laurent, Michel, Olivier, Comon, Pierre
This paper proposes an original approach to cluster multi-component data sets with an estimation of the number of clusters. From the construction of a minimal spanning tree with Prim's algorithm and...
Gradient based Approximate Joint Diagonalization by Orthogonal Transforms (2008)
Sorensen, Mikael, Icart, Sylvie, Comon, Pierre, Deneire, Luc
Approximate Joint Diagonalization (AJD) of a set of symmetric matrices by an orthogonal transform is a popular problem in Blind Source Separation (BSS). In this paper we propose a gradient based...
Galluccio, Laurent, Michel, Olivier, Comon, Pierre
This paper proposes an original approach to cluster multi-component data sets with an estimation of the number of clusters. From the construction of a minimal spanning tree with Prim's algorithm and...
Gradient based Approximate Joint Diagonalization by Orthogonal Transforms (2008)
Sorensen, Mikael, Icart, Sylvie, Comon, Pierre, Deneire, Luc
Approximate Joint Diagonalization (AJD) of a set of symmetric matrices by an orthogonal transform is a popular problem in Blind Source Separation (BSS). In this paper we propose a gradient based...
Ghosh, Aurorata, Tsigaridas, Elias, Descoteaux, Maxime, Comon, Pierre, Mourrain, Bernard, Deriche, Rachid
In this paper we extract the geometric characteristics from an antipodally symmetric spherical function (ASSF), which can be de- scribed equivalently in the spherical harmonic (SH) basis, in the...
Ghosh, Aurorata, Tsigaridas, Elias, Descoteaux, Maxime, Comon, Pierre, Mourrain, Bernard, Deriche, Rachid
In this paper we extract the geometric characteristics from an antipodally symmetric spherical function (ASSF), which can be de- scribed equivalently in the spherical harmonic (SH) basis, in the...
Cumulant matching for independent source extraction (2008)
Phlypo, Ronald, Zarzoso, Vicente, Comon, Pierre, Lemahieu, Ignace
In this work we show how one can make use of priors on signal statistics under the form of cumulant guesses to extract an independent source from an observed mixture. The advantage of using...
A contrast for independent component analysis with priors on the source kurtosis signs (2008)
Zarzoso, Vicente, Phlypo, Ronald, Comon, Pierre
A contrast function for independent component analysis (ICA) is presented incorporating the prior knowledge on the sub-Gaussian or super-Gaussian character of the sources as described by their...
ICA: A Potential Tool for BCI Systems (2008)
Kachenoura, Amar, Albera, Laurent, Senhadji, Lotfi, Comon, Pierre
Several studies dealing with independent component analysis (ICA)-based brain-computer interface (BCI) systems have been reported. Most of them have only explored a limited number of ICA methods,...
BLIND SOURCE SEPARATION: (2007)
Pierre Comon, Ludwig Rota, Is Laboratory
Blind Separation of convolutive mixtures and Blind Equalization of Multiple-Input Multiple-Output (MIMO) channels are two different ways of naming the same problem, which we address here. A novel...
Closed-form blind channel identification with MSK inputs (2007)
Pierre Comon, Olivier Grellier, Bernard Mourrain
Blind equalization of non minimumphase FIR channels requires prior identification, for stability reasons. We present a novel algorithm able to identify a channel in presence of an unknown MSK...
Blind MIMO equalization and joint-diagonalization criteria (2007)
We consider the problem of convolutive blind signal separation through the optimization of contrast functions. In this work, we show that some links between contrasts and joint diagonalization...
LACI : un outil pour les Interfaces Cerveau-Machine (2007)
Kachenoura, Amar, Albera, Laurent, Senhadji, Lotfi, Comon, Pierre
Résumé La majorité des études utilisant lACI pour les systèmes BCI exploitent soit FastICA soit INFOMAX, sans réelle justification. Lobjectif de notre article est d'attirer lattention...
LACI : un outil pour les Interfaces Cerveau-Machine (2007)
Kachenoura, Amar, Albera, Laurent, Senhadji, Lotfi, Comon, Pierre
Résumé La majorité des études utilisant lACI pour les systèmes BCI exploitent soit FastICA soit INFOMAX, sans réelle justification. Lobjectif de notre article est d'attirer lattention...
L'ACI : un outil pour les Interfaces Cerveau-Machine (2007)
KACHENOURA, Amar, ALBERA, Laurent, SENHADJI, Lotfi, COMON, Pierre
La majorité des études utilisant l'ACI pour les systèmes BCI exploitent soit FastICA soit INFOMAX, sans réelle justification. L'objectif de notre article est d'attirer l'attention des...
SAUD, un algorithme d'ICA par déflation semi-algébrique (2007)
ALBERA, Laurent, COMON, Pierre, XU, Hong
Nous proposons dans cet article une nouvelle technique d'ICA baptisée SAUD (Semi-Algebraic Unitary Deflation) et basée sur une procédure de déflation unitaire semi-algébrique. SAUD permet ainsi...
Séparation aveugle de sources dépendantes (2007)
Cette communication considère le problème de la séparation aveugle de sources pour un modèle de mélange linéaire instantané. La nouveauté réside dans la considération de sources non...
Blind Separation of Instantaneous Mixtures of Dependent Sources (2007)
This paper deals with the problem of Blind Source Separation. Contrary to the vast majority of works, we do not assume the statistical independence between sources and explicitly consider that they...
Blind Separation of Instantaneous Mixtures of Dependent Sources (2007)
This paper deals with the problem of Blind Source Separation. Contrary to the vast majority of works, we do not assume the statistical independence between sources and explicitly consider that they...
P.: Optimal step-size constant modulus algorithm (2007)
Abstract — The step size leading to the absolute minimum of the constant modulus (CM) criterion along the search direction can be obtained algebraically at each iteration among the roots of a...
L’ACI : un outil pour les Interfaces Cerveau-Machine (2007)
Kachenoura, Amar, Albera, Laurent, Senhadji, Lotfi, Comon, Pierre
Résumé – La majorité des études utilisant l’ACI pour les systèmes BCI exploitent soit FastICA soit INFOMAX, sans réelle justification. L’objectif de notre article est d'attirer...
Generic and Typical Ranks of Three-Way Arrays (2006)
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...
Blind Identification of Under-Determined Mixtures based on the Characteristic Fucntion (2006)
Linear Mixtures of independent random variables (the so-called sources) are sometimes referred to as Under-Determined Mixtures (UDM) when the number of sources exceeds the dimension of the...
Zarzoso, Vicente, Comon, Pierre
The present contribution deals with the statistical tool of Independent Component Analysis (ICA). The focus is on the deflation approach, whereby the independent components are extracted one after...
Generic Properties of Symmetric Tensors (2006)
Little has been published about rank-revealing decompositions of symmetric tensors. Definitions of rank are discussed, and useful results on Generic Rank are proved, with the help of tools borrowed...
Independent Component Analysis viewed as a Tensor Decomposition (2006)
The problem of identifying linear mixtures of independent random variables only from outputs can be traced back to 1953 with the works of Darmois or Skitovich. They pointed out that when data are non...
Genericity and Rank Deficiency of High Order Symmetric Tensors (2006)
Comon, Pierre, Mourrain, Bernard, Lim, Lek-Heng, Golub, Gene
Blind Identification of Under-Determined Mixtures (UDM) is involved in numerous applications, including Multi-Way factor Analysis (MWA) and Signal Processing. In the latter case, the use of...
Blind Identification of Under-Determined Mixtures based on the Characteristic Function (2006)
Linear Mixtures of independent random variables (the so-called sources) are sometimes referred to as Under-Determined Mixtures (UDM) when the number of sources exceeds the dimension of the...
Blind Identification of Under-Determined Mixtures based on the Characteristic Function (2006)
Linear Mixtures of independent random variables (the so-called sources) are sometimes referred to as Under-Determined Mixtures (UDM) when the number of sources exceeds the dimension of the...
Symmetric tensors and symmetric tensor rank (2006)
Pierre Comon, Gene Golub, Lek-heng Lim, Bernard Mourrain
Abstract. A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric...
M.: How fast is FastICA (2006)
Vicente Zarzoso, Pierre Comon, Mariem Kallel
The present contribution deals with the statistical tool of Independent Component Analysis (ICA). The focus is on the deflation approach, whereby the independent components are extracted one after...
Blind and Semi-Blind Equalization based on the Constant Power Criterion (2005)
Zarzoso, Vicente, Comon, Pierre
This paper focuses on the constant power (CP) criterion for blind linear equalization of digital communication channels. This recently proposed criterion is specially designed for the extraction of...
ICAR, a Tool for Blind Source Separation using Fourth Order Statistics Only (2005)
Albera, Laurent, Ferreol, Anne, Chevalier, Pascal, Comon, Pierre
The problem of blind separation of overdetermined mixtures of sources, that is, with fewer sources than (or as many sources as) sensors, is addressed in this paper. A new method, named ICAR...
Tensor ranks and some properties of tensor spaces (2005)
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...
Enhanced Line Search: a Novel Method to Accelerate PARAFAC (2005)
The ALS algorithm, used to fit the PARAFAC model, sometimes needs a large number of iterations before converging. The slowness in convergence can be due to the large size of the data, or to the...
Independent Component Analysis and Multi-Way Factor Analysis (2005)
Tutorial TUT-10: Independent Component Analysis and multiway factor analysis Instructor P. Comon; Research Director at CNRS, University of Nice, France Time & Location Saturday, March 19, 13:30 -...
Recherche linéaire optimisée : Une nouvelle méthode pour accélérer PARAFAC (2005)
L'algorithme des moindres carrés alternés (ALS), utilisé dans la décomposition de PARAFAC, peut nécessiter un très grand nombre d'itérations avant de converger. Cette lenteur de convergence...
Déflation parallèle avec des contrastes APF pour l'extraction aveugle de sources (2005)
ZARZOSO, Vicente, ROTA, Ludwig, COMON, Pierre
- Le présent article aborde le problème de la séparation de sources discrètes, notamment dans le cas sous-déterminé où il existe moins de capteurs que de sources. Les contrastes APF (alphabet...
Blind identification of under-determined mixtures based on the characteristic function (2005)
Linear mixtures of independent random variables (the so-called sources) are sometimes referred to as under-determined mixtures (UDM) when the number of sources exceeds the dimension of the...
Blind identification of under-determined mixtures based on the characteristic function (2005)
Linear Mixtures of independent random variables (the so-called sources) are sometimes referred to as Under-Determined Mixtures (UDM) when the number of sources exceeds the dimension of the...
channel equalization with algebraic optimal step size (2005)
The constant modulus algorithm (CMA) is arguably the most widespread iterative method for blind equalization of digital communication channels. The present contribution studies a recently proposed...
P.: Blind and semi-blind equalization based on the constant power criterion (2005)
Vicente Zarzoso, Pierre Comon, Senior Member
Abstract—This paper focuses on the constant power (CP) criterion for blind linear equalization of digital communication channels. This recently proposed criterion is specially designed for the...
Enhanced line search: A novel method to accelerate Parafac (2005)
www.i3s.unice.fr The ALS algorithm, used to fit the PARAFAC model, sometimes needs a large number of iterations before converging. The slowness in convergence can be due to the large size of the...
On the virtual array concept for higher order array processing (2005)
Pascal Chevalier, Laurent Albera, Anne Ferréol, Pierre Comon, Senior Member
Abstract—For about two decades, many fourth order (FO) array processing methods have been developed for both direction finding and blind identification of non-Gaussian signals. One of the main...
Blind Identification of Overcomplete Mixture of Sources (BIOME) (2004)
Albera, Laurent, Ferreol, Anne, Comon, Pierre, Chevalier, Pascal
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...
Canonical Tensor Decompositions (2004)
The Singular Value Decomposition (SVD) may be extended to tensors at least in two very different ways. One is the High-Order SVD (HOSVD), and the other is the Canonical Decomposition (CanD). Only the...
Contrasts, Independent Component Analysis, and Blind Deconvolution (2004)
A general definition of contrast criteria is proposed, which induces the concept of trivial filters. These optimization criteria enjoy identifiability properties, and aim at delivering outputs...
Blind identification of overcomplete mixtures of sources (2004)
Laurent Albera, Anne Ferréol, Pierre Comon, Pascal Chevalier
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...
Blind Identification of Under-determined Complex Mixtures of Independent Sources (2003)
This paper is devoted to under-determined linear mixtures of independent random variables (i.e. with more inputs than outputs). Blind identifiability of general under-determined mixtures is first...
Blind Identification of Underdetermined Mixtures based on the Hexacovariance (2003)
Albera, Laurent, Comon, Pierre, Chevalier, Pascal, Ferreol, Anne
Static linear mixtures with more sources than sensors are considered. Blind Identification (BI) of underdetermined mixtures is addressed by taking advantage of Sixth Order (SixO) statistics and the...
Linear Mixtures of independent random variables (the so-called sources) are sometimes referred to as Under-Determined Mixtures (UDM) when the number of sources exceeds the dimension of the...
We introduce a novel algebraic approach to solving some problems arising is signal processing and digital communications. These problems can be described or reduced to systems of mukltivariate...
ICAR, un algorithme d'ICA à convergence rapide, robuste au bruit (2003)
ALBERA, Laurent, FERREOL, Anne, CHEVALIER, Pascal, COMON, Pierre
- Une nouvelle méthode de séparation aveugle de sources, baptisée ICAR et n'exploitant que les statistiques d'ordre 4 des observations, est proposée. Cette dernière est comparée par simulations...
Séparation de signaux ZCM : application en radar SSR (2003)
PETROCHILOS, Nicolas, COMON, Pierre
Une étude statistique des réponses des radars secondaires de surveillance démontre leur pseudo-gaussianité à l'ordre cinq. Une conséquence est que l'on ne peut pas faire confiance aux méthodes...
Critères de contraste déterministes pour la séparation de sources (2003)
- La séparation aveugle de sources est souvent menée sous l'hypopthèse que les sources sont statistiquement indépendantes. Cependant, cette hypothèse n'est pas indispensable, et peut être...
Une approche algébrique de l'identification aveugle de canaux de communications (2003)
- Dans cet article est présentée une nouvelle approche au problème de l'identification aveugle de canaux SISO de communications pour les modulations de type PSK. L'intérêt majeur de cette...
Égalisation aveugle de mélanges convolutifs MIMO (2003)
ROTA, Ludwig, COMON, Pierre, ICART, Sylvie
- Cet article décrit un nouvel algorithme d'égalisation aveugle pour des mélanges convolutifs MIMO. Une factorisation de l'égaliseur, sous forme de rotations planes et de retards purs, est...
Sixth order blind identification of underdetermined mixtures (BIRTH) of sources (2003)
Laurent Albera, Anne Ferréol, Pierre Comon, Pascal Chevalier
Static linear mixtures with more sources than sensors are considered. The Blind Source Identification (BSI) of underdetermined mixtures problem is addressed by taking advantage of Sixth Order (SixO)...
We present a partial survey of the tools borrowed from tensor algebra, which have been utilized recently in Statistics and Signal Processing. It is shown why the decompositions well known in linear...
We present a partial survey of the tools borrowed from tensor algebra, which have been utilized recently in Statistics and Signal Processing. It is shown why the decompositions well known in linear...
Tensor Decompositions, State of the Art and Applications (2002)
In this paper, we present a partial survey of the tools borrowed from tensor algebra, which have been utilized recently in Statistics and Signal Processing. It is shown why the decompositions well...
Tensor Decompositions, State of the Art and Applications (2002)
In this paper, we present a partial survey of the tools borrowed from tensor algebra, which have been utilized recently in Statistics and Signal Processing. It is shown why the decompositions well...
Analytical blind channel identification (2002)
Olivier Grellier, Pierre Comon, Senior Member, Bernard Mourrain
Abstract—In this paper, a novel analytical blind single-input single-output (SISO) identification algorithm is presented, based on the noncircular second-order statistics of the output. It is shown...
Wide-sense polynomial equalizers in digital communications (2001)
On propose dans cet article un Egaliseur Polynômial au Sens Large (WSPE), dédié aux canaux spéculaires. En se basant sur la distribution QPSK des entrées, largement utilisée en communications...
Séparation de mélanges convolutifs par diagonalisation conjointe (2001)
COMON, Pierre, MOREAU, Eric, ROTA, Ludwig
La séparation aveugle de mélanges convolutifs et l'égalisation aveugle de canaux à entrées et sorties multiples sont un seul et même sujet, que nous abordons ici. L'algorithme numérique,...
Blind separation of convolutive mixtures: a contrast-based joint diagonalization approach (2001)
Pierre Comon, Éric Moreau, Ludwig Rota
Blind Separation of convolutive mixtures and Blind Equalization of Multiple-Input Multiple-Output (MIMO) channels are two different ways of naming the same problem, which we address here. The...
Blind separation of convolutive mixtures: a contrast-based joint diagonalization approach (2001)
Pierre Comon, Eric Moreau, Ludwig Rota
Blind Separation of convolutive mixtures and Blind Equalization of Multiple-Input Multiple-Output (MIMO) channels are two different ways of naming the same problem, which we address here. The...
ML estimation of SSR signals, identifiability, and Cramer-Rao bounds (2000)
Nicolas Petrochilos, Pierre Comon
ABSTRACT In this article, a Maximum Likelihood method is applied to Secondary Surveillance Radar (SSR) signals impinging on an M-element antenna. At base-band, a SSR signal consists of a binary...
Egalisation en présence de sources discrètes (1999)
GRELLIER, Olivier, COMON, Pierre
Ces dernières années, l'égalisation aveugle de canaux de communication a suscité un grand intérêt, entre autres parce qu'elle permet d'accroître le débit. De nombreux algorithmes itératifs...
Closed-form equalization (1999)
Olivier Grellier, Pierre Comon
Many blind or semi-blind equalizers are implemented with the help of iterative algorithms, and therefore may require long convergene times or suffer from local minima. Closedform block blind...
Non linear inversion of underdetermined mixtures (1999)
Pierre Comon, Olivier Grellier
Static linear mixtures with fewer sensors than sources are considered. They are encountered for instance in downlink radio communications, if the spectral e-ciency is attempted to be improved. The...
Autocalibration analytique d'antenne (1997)
GRELLIER, Olivier, COMON, Pierre
On présente une nouvelle méthode d'autocalibration (i.e. sans source coopérante) basée sur le fait que les vecteurs directionnels sont de module unité. Un premier algorithme est proposé, et...
CAPDEVIELLE, Véronique, CHEVALIER, Pascal, CALVARY, Philippe, COMON, Pierre
Depuis une dizaine d'années, les méthodes de séparation aveugle de sources aux ordres supérieurs ne cessent de se développer. Plus récemment, un certain nombre de résultats concernant le...
Statistiques d'ordre supérieur pour le traitement du signal (1997)
Lacoume, Jean-Louis, Amblard, Pierre-Olivier, Comon, Pierre
Table des matieres de ce livre maintenant en telechargement libre: (1) Introduction aux atatistiques d'ordre superieur, (2) Multicorrelations et multispectres, (3) Signaux et systemes, (4) Signaux...
Statistiques d'ordre supérieur pour le traitement du signal (1997)
Lacoume, Jean-Louis, Amblard, Pierre-Olivier, Comon, Pierre
Table des matieres de ce livre maintenant en telechargement libre: (1) Introduction aux atatistiques d'ordre superieur, (2) Multicorrelations et multispectres, (3) Signaux et systemes, (4) Signaux...
Independent Component Analysis, A Survey Of Some Algebraic Methods. (1996)
Jean-François Cardoso, Pierre Comon
The source separation problem has been addressed in many ways during the last decade, and one of its instances gave birth to Independent Component Analysis (ICA). Iterative methods can be opposed to...
Structured matrices and inverses (1995)
A matrix (and any associated linear system) will be referred to as structured if it has a small displacement rank. It is known that the inverse of a structured matrix is structured, which allows fast...
Structured matrices and inverses (1995)
A matrix (and any associated linear system) will be referred to as structured if it has a small displacement rank. It is known that the inverse of a structured matrix is structured, which allows fast...
Supervised classification: a probabilistic approach (1995)
In this tutorial, some classical tools of data analysis -- and others less well known -- are surveyed in detail, that can be applied to supervised classification, and in particular to learning with...
Joos V, Lieven De Lathauwer, Pierre Comon
Abstr act − Two new generalizations of tenso r concepts for signa l processing are presented. These generalizatio ns are typically relev ant for appli cations where one tenso r consi sts of valua...
Estimation of performance bounds in supervised classification (1994)
Pierre Comon, Jean-luc Voz, Michel Verleysen
Abstract. The Bayes theory gives the ultimate performances that can be reached in a classification problem. We present in this paper a method that allows to estimate these performance bounds given...
Remarques sur la diagonalisation tensorielle par la méthode de Jacobi (1993)
Le problème de "séparation de sources" est soluble en recourrant uniquement aux statistiques d'ordre 2, comme nous le soulignons. Pourtant, les conditions d'identifiabilité imposent souvent...
Independent Component Analysis (1992)
The Independent Component Analysis (ICA) of a random vector consists of searching for the linear transformation that minimizes the statistical dependence between its components. In order to design a...
Independent Component Analysis (1992)
The Independent Component Analysis (ICA) of a random vector consists of searching for the linear transformation that minimizes the statistical dependence between its components. In order to design a...
Elsevier Short communication (1991)
Abstract. The algorithm proposed aims to identify moving average coefficient matrices of an MA process, not necessarily minimum-phase, driven by an unobserved non-gaussian input. It is assumed that...
Elsevier Blind separation of sources, Part II " Problems statement (1990)
Pierre Comon, Christian Jutten, Jeanny Herault
Abstract. Though it arouses more and more curiosity, the HJ iterative algorithm has never been derived in mathematical terms to date. We attempt in this paper to describe it from a statistical point...
Extrapolation des signaux lacunaires (1983)
COMON, Pierre, LEJEUNE, Gérard
Les signaux fortement perturbés par endroits ne sont pas toujours traitables par les méthodes classiques de filtrage. Nous nous proposons de nous ramener à un signal "lacunaire" en annulant...