BMICA-independent component analysis based on B-spline mutual information estimator

The information theoretic concept of mutual information provides a general framework to evaluate dependencies between variables. Its estimation however using B-Spline has not been used before in creating an approach for Independent Component Analysis. In this paper we present a B-Spline estimator for mutual information to find the independent components in mixed signals. Tested using electroencephalography (EEG) signals the resulting BMICA (B-Spline Mutual Information Independent Component Analysis) exhibits better performance than the standard Independent Component Analysis algorithms of FastICA, JADE, SOBI and EFICA in similar simulations. BMICA was found to be also more reliable than the 'renown' FastICA

Nonlinear estimators from ICA mixture models

"NOTICE: this is the author's version of a work that was accepted for publication in Signal Processing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Signal Processing, 155, (2019) https://doi.org/10.1016/j.sigpro.2018.10.003"[EN] Independent Component Analyzers Mixture Models (ICAMM) are versatile and general models for a large variety of probability density functions. In this paper we assume ICAMM to derive new MAP and LMSE estimators. The first one (MAP-ICAMM) is obtained by an iterative gradient algorithm, while the second (LMSE-ICAMM) admits a closed-form solution. Both estimators can be combined by using LMSE-ICAMM to initialize the iterative computation of MAP-ICAMM .The new estimators are applied to the reconstruction of missed channels in EEG multichannel analysis. The experiments demonstrate the superiority of the new estimators with respect to: Spherical Splines, Hermite, Partial Least Squares, Support Vector Regression, and Random Forest Regression. (C) 2018 Elsevier B.V. All rights reserved.This work was supported by Spanish Administration (Ministerio de Economia y Competitividad) and European Union (FEDER) under grant TEC2014-58438-R, and Generalitat Valenciana under grant PROMETEO II/2014/032.Safont Armero, G.; Salazar Afanador, A.; Vergara Domínguez, L.; Rodriguez Martinez, A. (2019). Nonlinear estimators from ICA mixture models. Signal Processing. 155:281-286. https://doi.org/10.1016/j.sigpro.2018.10.003S28128615

Neural Connectivity with Hidden Gaussian Graphical State-Model

The noninvasive procedures for neural connectivity are under questioning. Theoretical models sustain that the electromagnetic field registered at external sensors is elicited by currents at neural space. Nevertheless, what we observe at the sensor space is a superposition of projected fields, from the whole gray-matter. This is the reason for a major pitfall of noninvasive Electrophysiology methods: distorted reconstruction of neural activity and its connectivity or leakage. It has been proven that current methods produce incorrect connectomes. Somewhat related to the incorrect connectivity modelling, they disregard either Systems Theory and Bayesian Information Theory. We introduce a new formalism that attains for it, Hidden Gaussian Graphical State-Model (HIGGS). A neural Gaussian Graphical Model (GGM) hidden by the observation equation of Magneto-encephalographic (MEEG) signals. HIGGS is equivalent to a frequency domain Linear State Space Model (LSSM) but with sparse connectivity prior. The mathematical contribution here is the theory for high-dimensional and frequency-domain HIGGS solvers. We demonstrate that HIGGS can attenuate the leakage effect in the most critical case: the distortion EEG signal due to head volume conduction heterogeneities. Its application in EEG is illustrated with retrieved connectivity patterns from human Steady State Visual Evoked Potentials (SSVEP). We provide for the first time confirmatory evidence for noninvasive procedures of neural connectivity: concurrent EEG and Electrocorticography (ECoG) recordings on monkey. Open source packages are freely available online, to reproduce the results presented in this paper and to analyze external MEEG databases