Catálogo de publicaciones - libros

We describe an ICA method based on second order statistics which was originally developed for the separation of components in astrophysical images but is appropriate in contexts where accuracy and versatility are of primary importance. It combines several basic ideas of ICA in a new flexible framework designed to deal with complex data scenarios. This paper describes our approach and discusses its implementation in terms of a .

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 consider that they are dependent. We introduce three particular models of dependent sources and show that their cumulants have interesting properties. Based on these properties, we investigate the behaviour of classical Blind Source Separation algorithms when applied to these sources: depending on the source vector, the separation may be sucessful or some additionnal indeterminacies can be identified.

This paper addresses the problem of the blind signal extraction of sources by means of an information theoretic and geometric criterion. Our main result is the extension of the minimum support criterion to the case of mixtures of complex signals. This broadens the scope of its possible applications in several fields, such as communications.

In this paper, we address the problem of blind source separation of non circular digital communication signals. A new Jacobi-like algorithm that achieves the joint diagonalization of a set of symmetric third-order tensors is proposed. The application to the separation of non-gaussian sources using fourth order cumulants is particularly investigated. Finally, computer simulations on synthetic signals show that this new algorithm improves the STOTD algorithm.

We propose a new algorithm to impose independence constraints in one mode of the CP model, and show with simulations that it outperforms the existing algorithm.

In this work, we deal with blind source separation of a class of nonlinear mixtures. The proposed method can be regarded as an adaptation of the solutions developed in [1,2] to the considered mixing system. Also, we provide a local stability analysis of the employed learning rule, which permits us to establish necessary conditions for an appropriate convergence. The validity of our approach is supported by simulations.

Independent Subspace Analysis (ISA) is a generalization of ICA. It tries to find a basis in which a given random vector can be decomposed into groups of mutually independent random vectors. Since the first introduction of ISA, various algorithms to solve this problem have been introduced, however a general proof of the uniqueness of ISA decompositions remained an open question. In this contribution we address this question and sketch a proof for the separability of ISA. The key condition for separability is to require the subspaces to be not further decomposable (irreducible). Based on a decomposition into irreducible components, we formulate a general model for ISA without restrictions on the group sizes. The validity of the uniqueness result is illustrated on a toy example. Moreover, an extension of ISA to subspace extraction is introduced and its indeterminacies are discussed.

This paper derives a new algorithm that performs independent component analysis (ICA) by optimizing the contrast function of the RADICAL algorithm. The core idea of the proposed optimization method is to combine the global search of a good initial condition with a gradient-descent algorithm. This new ICA algorithm performs faster than the RADICAL algorithm (based on Jacobi rotations) while still preserving, and even enhancing, the strong robustness properties that result from its contrast.

Given a time series of multicomponent measurements of an evolving stimulus, nonlinear blind source separation (BSS) usually seeks to find a “source” time series, comprised of statistically independent combinations of the measured components. In this paper, we seek a source time series that has a density function equal to the product of density functions of individual components. In an earlier paper, it was shown that the phase space density function induces a Riemannian geometry on the system’s state space, with the metric equal to the local velocity correlation matrix of the data. From this geometric perspective, the vanishing of the curvature tensor is a necessary condition for BSS. Therefore, if this data-derived quantity is non-vanishing, the observations are not separable. However, if the curvature tensor is zero, there is only one possible set of source variables (up to transformations that do not affect separability), and it is possible to compute these explicitly and determine if they do separate the phase space density function. A longer version of this paper describes a more general method that performs nonlinear multidimensional BSS or independent subspace separation.

A framework named copula component analysis (CCA) for blind source separation is proposed as a generalization of independent component analysis (ICA). It differs from ICA which assumes independence of sources that the underlying components may be dependent by certain structure which is represented by Copula. By incorporating dependency structure, much accurate estimation can be made in principle in the case that the assumption of independence is invalidated. A two phrase inference method is introduced for CCA which is based on the notion of multi-dimensional ICA. Simulation experiments preliminarily show that CCA can recover dependency structure within components while ICA does not.