Recurrent networks for separating extractable-target nonlinear mixtures. Part I: non-blind configurations

International audienceWhile most reported source separation methods concern linear mixtures, we here address the nonlinear case. Even for a known nonlinear mixing model, creating a system which implements the exact inverse of this model is not straightforward for most nonlinear models. We first define a large class of possibly nonlinear models, i.e. "additive-target mixtures" (ATM), for which this inversion may be achieved thanks to the nonlinear recurrent networks that we propose to this end. We then further extend this approach to the "extractable-target mixtures" (ETM) that we also introduce in this paper. We illustrate these general approaches for two specific classes of mixtures, i.e. linear-quadratic mixtures, and quadratic ones. We then focus on our networks suited to linear-quadratic mixtures and we provide a detailed analysis of their equilibrium points and their stability. This allows us to introduce an automated procedure for selecting their free weights so as to guarantee the stability of a separating point for any source signals. Test results show the effectiveness of this approach for various types of source signals

A Blind Source Separation Method for Chemical Sensor Arrays based on a Second-order mixing model

International audienceIn this paper we propose a blind source separation method to process the data acquired by an array of ion-selective electrodes in order to measure the ionic activity of different ions in an aqueous solution. While this problem has already been studied in the past, the method presented differs from the ones previously analyzed by approximating the mixing function by a second-degree polynomial, and using a method based on the differential of the mutual information to adjust the parameter values. Experimental results, both with synthetic and real data, suggest that the algorithm proposed is more accurate than the other models in the literature

Theoretical Studies and Algorithms Regarding the Solution of Non-invertible Nonlinear Source Separation

International audienceIn this paper, we analyse and solve a source separation problem based on a mixing model that is nonlinear and non-invertible at the space of mixtures. The model is relevant considering it may represent the data obtained from ion-selective electrode arrays. We apply a new approach for solving the problems of local stability of the recurrent network previously used in the literature, which allows for a wider range of source concentration. In order to achieve this, we utilize a second-order recurrent network which can be shown to be locally stable for all solutions. Using this new network and the priors that chemical sources are continuous and smooth, our proposal performs better than the previous approach

Biologically-Plausible Determinant Maximization Neural Networks for Blind Separation of Correlated Sources

Extraction of latent sources of complex stimuli is critical for making sense of the world. While the brain solves this blind source separation (BSS) problem continuously, its algorithms remain unknown. Previous work on biologically-plausible BSS algorithms assumed that observed signals are linear mixtures of statistically independent or uncorrelated sources, limiting the domain of applicability of these algorithms. To overcome this limitation, we propose novel biologically-plausible neural networks for the blind separation of potentially dependent/correlated sources. Differing from previous work, we assume some general geometric, not statistical, conditions on the source vectors allowing separation of potentially dependent/correlated sources. Concretely, we assume that the source vectors are sufficiently scattered in their domains which can be described by certain polytopes. Then, we consider recovery of these sources by the Det-Max criterion, which maximizes the determinant of the output correlation matrix to enforce a similar spread for the source estimates. Starting from this normative principle, and using a weighted similarity matching approach that enables arbitrary linear transformations adaptable by local learning rules, we derive two-layer biologically-plausible neural network algorithms that can separate mixtures into sources coming from a variety of source domains. We demonstrate that our algorithms outperform other biologically-plausible BSS algorithms on correlated source separation problems.Comment: NeurIPS 2022, 37 page

A stochastic algorithm for probabilistic independent component analysis

The decomposition of a sample of images on a relevant subspace is a recurrent problem in many different fields from Computer Vision to medical image analysis. We propose in this paper a new learning principle and implementation of the generative decomposition model generally known as noisy ICA (for independent component analysis) based on the SAEM algorithm, which is a versatile stochastic approximation of the standard EM algorithm. We demonstrate the applicability of the method on a large range of decomposition models and illustrate the developments with experimental results on various data sets.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS499 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org