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.

A simple and flexible technique for improving the modeling and predistortion of power amplifiers is presented. The technique, which relies on the sparsity assumption for the kernel coefficients of the full Volterra (FV) behavioral model, combines a greedy algorithm for the selection of the active coefficients, a maximum likelihood method for their estimation and an information criterion for determining the best model. The approach has been applied to the design of reduced-parameters FV-based digital predistorters for three power amplifiers driven with orthogonal frequency division multiplexing signals, following the LTE and DVB-T2 standards, and a multichannel wideband code-division multiple access signal. Results show that the proposed linearizers meet the spectral masks and error vector magnitude constraints of the referred standards and provide a reduction better than 45% in the number of parameters, compared to the FV predistorters.

In this letter, we propose a novel least-mean-square (LMS) algorithm for filtering speech sounds in the adaptive noise cancellation (ANC) problem. It is based on the minimization of the squared Euclidean norm of the difference weight vector under a stability constraint defined over the a posteriori estimation error. To this purpose, the Lagrangian methodology has been used in order to propose a nonlinear adaptation rule defined in terms of the product of differential inputs and errors which means a generalization of the normalized (N)LMS algorithm. The proposed method yields better tracking ability in this context as shown in the experiments which are carried out on the AURORA 2 and 3 speech databases. They provide an extensive performance evaluation along with an exhaustive comparison to standard LMS algorithms with almost the same computational load, including the NLMS and other recently reported LMS algorithms such as the modified (M)-NLMS, the error nonlinearity (EN)-LMS, or the normalized data nonlinearity (NDN)-LMS adaptation.

This study presents a blind and geometric technique which pursues the linear decomposition of the observations in bounded component signals. The bounded component analysis of the observations relies on the hypotheses of compactness and Cartesian decomposition of the convex support of the vector of component signals, and in the invertibility of the mixture. Assumptions, which in absence of noise, are able to guarantee the identifiability of the mixture and separability of the components, up to permutation, scaling, and phase ambiguities. Under these conditions, the convex perimeter of the normalized linear combination of the observations is shown to be a global contrast function whose minima correspond with the extraction of bounded components of the observations. Practical extraction and separation algorithms based on the minimization of this criterion are given. The experimental results with communications signals serve to illustrate the good performance of the proposed method in high SNR scenarios, even for a small number of samples.

This work reviews and extends a family of log-determinant (log-det) divergences for symmetric positive definite (SPD) matrices and discusses their fundamental properties. We show how to use parameterized Alpha-Beta (AB) and Gamma log-det divergences to generate many well-known divergences; in particular, we consider the Stein’s loss, the S-divergence, also called Jensen-Bregman LogDet (JBLD) divergence, Logdet Zero (Bhattacharyya) divergence, Affine Invariant Riemannian Metric (AIRM), and other divergences. Moreover, we establish links and correspondences between log-det divergences and visualise them on an alpha-beta plane for various sets of parameters. We use this unifying framework to interpret and extend existing similarity measures for semidefinite covariance matrices in finite-dimensional Reproducing Kernel Hilbert Spaces (RKHS). This paper also shows how the Alpha-Beta family of log-det divergences relates to the divergences of multivariate and multilinear normal distributions. Closed form formulas are derived for Gamma divergences of two multivariate Gaussian densities; the special cases of the Kullback-Leibler, Bhattacharyya, Rényi, and Cauchy-Schwartz divergences are discussed. Symmetrized versions of log-det divergences are also considered and briefly reviewed. Finally, a class of divergences is extended to multiway divergences for separable covariance (or precision) matrices.

In this paper we present an iterative inversion (II) approach to blind source separation (BSS). It consists of a quasi-Newton method for the resolution of an estimating equation obtained from the implicit inversion of a robust estimate of the mixing system. The resulting learning rule includes several existing algorithms for BSS as particular cases giving them a novel and unified interpretation.It also provides a justification of the Cardoso and Laheld step size normalization. The II method is first presented for instantaneous mixtures and then extended to the problem of blind separation of convolutive mixtures. Finally, we derive the necessary and sufficient asymptotic stability conditions for both the instantaneous and convolutive methods to converge.