Combining blind source extraction with joint approximate diagonalization: Thin algorithms for ICA

In this paper a multivariate contrast function is proposed for the blind signal extraction of a subset of the indepen dent components from a linear mixture. This contrast com bines the robustness of the joint approximate diagonaliza tion techniques with the flexibility of the methods for blind signal extraction. Its maximization leads to hierarchical and simultaneous ICA extraction algorithms which are respec tively based on the thin QR and thin SVD factorizations. The interesting similarities and differences with other exist ing contrasts and algorithms are commented.Comisión Interministerial de Ciencia y Tecnología (CICYT). España TIC2001-0751-C04-0

Globally convergent Newton algorithms for blind decorrelation

This paper presents novel Newton algorithms for the blind adaptive decorrelation of real and complex processes. They are globally convergent and exhibit an interesting relation ship with the natural gradient algorithm for blind decorre lation and the Goodall learning rule. Indeed, we show that these two later algorithms can be obtained from their New ton decorrelation versions when an exact matrix inversion is replaced by an iterative approximation to it.Comisión Interministerial de Ciencia y Tecnología (CICYT). España TIC2001-0751-C04-0

A Joint Optimization Criterion for Blind DS-CDMA Detection

This paper addresses the problem of the blind detection of a desired user in an asynchronous DS-CDMA communications system with multipath propagation channels. Starting from the inverse filter criterion introduced by Tugnait and Li in 2001, we propose to tackle the problem in the context of the blind signal extraction methods for ICA. In order to improve the performance of the detector, we present a criterion based on the joint optimization of several higher-order statistics of the outputs. An algorithm that optimizes the proposed criterion is described, and its improved performance and robustness with respect to the near-far problem are corroborated through simulations. Additionally, a simulation using measurements on a real software-radio platform at 5 GHz has also been performed.Ministerio de Ciencia y tecnología TEC2004-06451-C05-0

Generalized Alpha-Beta Divergences and Their Application to Robust Nonnegative Matrix Factorization

We propose a class of multiplicative algorithms for Nonnegative Matrix Factorization (NMF) which are robust with respect to noise and outliers. To achieve this, we formulate a new family generalized divergences referred to as the Alpha-Beta-divergences (AB-divergences), which are parameterized by the two tuning parameters, alpha and beta, and smoothly connect the fundamental Alpha-, Beta- and Gamma-divergences. By adjusting these tuning parameters, we show that a wide range of standard and new divergences can be obtained. The corresponding learning algorithms for NMF are shown to integrate and generalize many existing ones, including the Lee-Seung, ISRA (Image Space Reconstruction Algorithm), EMML (Expectation Maximization Maximum Likelihood), Alpha-NMF, and Beta-NMF. Owing to more degrees of freedom in tuning the parameters, the proposed family of AB-multiplicative NMF algorithms is shown to improve robustness with respect to noise and outliers. The analysis illuminates the links of between AB-divergence and other divergences, especially Gamma- and Itakura-Saito divergences

Information Theory Applications in Signal Processing

Ministerio de Economía, Industria y Competitividad (MINECO) TEC2017-82807-PMinisterio de Economía, Industria y Competitividad (MINECO) TEC2014-53103-

Centroid-Based Clustering with ab-Divergences

Centroid-based clustering is a widely used technique within unsupervised learning algorithms in many research fields. The success of any centroid-based clustering relies on the choice of the similarity measure under use. In recent years, most studies focused on including several divergence measures in the traditional hard k-means algorithm. In this article, we consider the problem of centroid-based clustering using the family of ab-divergences, which is governed by two parameters, a and b. We propose a new iterative algorithm, ab-k-means, giving closed-form solutions for the computation of the sided centroids. The algorithm can be fine-tuned by means of this pair of values, yielding a wide range of the most frequently used divergences. Moreover, it is guaranteed to converge to local minima for a wide range of values of the pair (a, b). Our theoretical contribution has been validated by several experiments performed with synthetic and real data and exploring the (a, b) plane. The numerical results obtained confirm the quality of the algorithm and its suitability to be used in several practical applications.MINECO TEC2017-82807-

Initialization method for speech separation algorithms that work in the time-frequency domain

This article addresses the problem of the unsupervised separa tion of speech signals in realistic scenarios. An initialization procedure is proposed for independent component analysis (ICA) algorithms that work in the time-frequency domain and require the prewhitening of the observations. It is shown that the proposed method drastically reduces the permuted solu tions in that domain and helps to reduce the execution time of the algorithms. Simulations confirm these advantages for several ICA instantaneous algo rithms and the effectiveness of the proposed technique in emulated reverber ant environments.Ministerio de Ciencia y tecnología (España) TEC2008-0625

Unsupervised Common Spatial Patterns

The common spatial pattern (CSP) method is a dimensionality reduction technique widely used in brain-computer interface (BCI) systems. In the two-class CSP problem, training data are linearly projected onto direc tions maximizing or minimizing the variance ratio between the two classes. The present contribution proves that kurto sis maximization performs CSP in an unsupervised manner, i.e., with no need for labeled data, when the classes follow Gaussian or elliptically symmetric distributions. Numerical analyses on synthetic and real data validate these findings in various experimental conditions, and demonstrate the interest of the proposed unsupervised approach.Ministerio de Economía y Competitividad (España) TEC2017-82807-

A Sparse-Bayesian Approach for the Design of Robust Digital Predistorters Under Power-Varying Operation

"Early access"In this article, a sparse-Bayesian treatment is proposed to solve the crucial questions posed by power amplifier (PA) and digital predistorter (DPD) modeling. To learn a model, the advanced Bayesian framework includes a group of specific processes that maximize the likelihood of the measured data: regressor pursuit and identification, coefficient estimation, stopping criterion, and regressor deselection. The relevance vector machine (RVM) method is reformulated theoretically to be implemented in complex-valued linear regression. In essence, given an initial set of candidate regressors, the result of this sparse-Bayesian learning approach is the most likely model. Experimental results are provided for the linearization of class AB and class J PAs driven by a 30-MHz fifth-generation new radio signal for a fixed average power, where the evolution of the figures of merit versus the number of active coefficients is examined for the proposed sparse-Bayesian pursuit (SBP) algorithm in comparison to other greedy algorithms. The SBP presents a good performance in terms of linearization capabilities and computational cost. Furthermore, the proposed Bayesian framework enabled the design of a DPD model structure, deselect regressors, and readjust coefficients in a direct learning architecture, demonstrating the robustness to changes in the power level over a 10-dB range.Ministerio de Ciencia e Innovación 10.13039/501100011033Junta de Andalucía - Fondos FEDER US-126499

Optimization of Alpha-Beta Log-Det Divergences and their Application in the Spatial Filtering of Two Class Motor Imagery Movements

The Alpha-Beta Log-Det divergences for positive definite matrices are flexible divergences that are parameterized by two real constants and are able to specialize several relevant classical cases like the squared Riemannian metric, the Steins loss, the S-divergence, etc. A novel classification criterion based on these divergences is optimized to address the problem of classification of the motor imagery movements. This research paper is divided into three main sections in order to address the above mentioned problem: (1) Firstly, it is proven that a suitable scaling of the class conditional covariance matrices can be used to link the Common Spatial Pattern (CSP) solution with a predefined number of spatial filters for each class and its representation as a divergence optimization problem by making their different filter selection policies compatible; (2) A closed form formula for the gradient of the Alpha-Beta Log-Det divergences is derived that allows to perform optimization as well as easily use it in many practical applications; (3) Finally, in similarity with the work of Samek et al. 2014, which proposed the robust spatial filtering of the motor imagery movements based on the beta-divergence, the optimization of the Alpha-Beta Log-Det divergences is applied to this problem. The resulting subspace algorithm provides a unified framework for testing the performance and robustness of the several divergences in different scenarios.Ministerio de Economía y Competitividad TEC2014-53103-