Sergio Cruces

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.

Robust blind source separation algorithms using cumulants

Abstract In this paper we propose a new approach to blind separation of independent source signals that, while avoiding the imposition of an orthogonal mixing matrix, is robust with respect to the existence of additive Gaussian noise in the mixture. We demonstrate that, for the wide class of source distributions with certain non-null cumulants and a pre-specified scaling, separation is always a saddle point of a cumulant-based cost function. We propose a quasi-Newton approach for determining this saddle point. This enables us to obtain a family of separation algorithms which, based on higher order statistics, yields unbiased estimates even in the presence of large Gaussian noise and has the interesting property of local isotropic convergence. Another family of algorithms that incorporates second-order statistics loses the former desirable convergence properties but it provides more precise estimates in the absence of noise. Extensive computer simulations confirm robustness and the excellent performance of the resulting algorithms.

Bounded Component Analysis of Linear Mixtures: A Criterion of Minimum Convex Perimeter

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.

Behavioral Modeling and Predistortion of Power Amplifiers Under Sparsity Hypothesis

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.

Novel blind source separation algorithms using cumulants

This paper investigates new algorithms for blind source separation that use cumulants instead of nonlinearities matched to the probability distribution of the sources. It is demonstrated that separation is a saddle point of a cumulant-based entropy cost function. To determine this point we propose two quasi-Newton algorithms whose convergence is isotropic and does not depend on the sources distribution. Moreover, convergence properties remain the same when there is Gaussian noise in the mixture.

The Minimum Support Criterion for Blind Signal Extraction: A Limiting Case of the Strengthened Young's Inequality

In this paper, we address the problem of the blind extraction of a subset of “interesting” independent signals from a linear mixture. We present a novel criterion for the extraction of the sources whose density has the minimum support measure. By extending the definition of the Renyi’s entropies to include the zero-order case, this criterion can be regarded as part of a more general entropy minimization principle. It is known that Renyi’s entropies provide contrast functions for the blind extraction of independent and identically distributed sources under an ∞-norm constraint on the global transfer system. The proposed approach gives sharper lower-bounds for the zero-order Renyi’s entropy case and, contrary to the existing results, it allows the extraction even when the sources are non identically distributed. Another interesting feature is that it is robust to the presence of certain kinds of additive noise and outliers in the observations.

Blind Separation of Dependent Sources With a Bounded Component Analysis Deflationary Algorithm

The problem of blind source separation of complex-valued sources from a linear mixture is addressed. We propose a deflationary algorithm for the sequential recovery of a set of communication signals, where each source is extracted by performing a Bounded Component Analysis of the linear mixture. The contribution of each recovered source to the observations is removed by minimizing its convex perimeter, without using second-order statistics. This implies to run a gradient descent algorithm several times. In order to accelerate the convergence, we have derived a fast step size that exploits the second-order information of the cost function by means of the augmented Hessian matrix. Computer simulations show that the proposed method is able to blindly separate even dependent sources, as long as they satisfy the BCA separability conditions. Also, the speed of convergence of this novel step size is compared with other classical approaches.

A Gauss-Newton method for blind source separation of convolutive mixtures

In this paper we present several Gauss-Newton algorithms for blind source separation of convolutive mixtures. The algorithms can be interpreted as generalizations of two previous approaches due to Van Gerven and Van Compernolle (1995) and Nguyen-Thi and Jutten (1995). Since they are of the Gauss-Newton type, they exhibit a fast rate of convergence. Also, we present a stability analysis for two sources and instantaneous mixtures where we show that the algorithms cannot converge to non-separating solutions.

Bounded Component Analysis of linear mixtures

The blind decomposition of the observations, as a set of additive components of simpler structure, is a problem with many applications in scientific and practical fields. Our study assumes that the component signals are of bounded nature, and relies on the geometric decomposition of the convex set that supports the observations as a Minkowski direct sum of the convex sets that support the components. This last property, which is weaker than the mutual independence of the additive components of the observations, is sufficient for the essential identifiability of the bounded and indecomposable components. In practice, it is usual that the components lie in one-dimensional complex subspaces. Therefore, for this case, we describe a sequential method for their recovery.

An application of ICA to blind DS-CDMA detection: a joint optimization criterion

This paper studies the application of the theory and algorithms of blind signal extraction to solve the problem of the detection of the desired users in a DS-CDMA communications system. Typically, the uplink in this system is characterized by users that transmit asynchronously and propagation channels that are multipath. We address inverse filter criterion introduced by Tugnait in [1] and we show that a prewhitening preprocessing approach together with the joint combination of several higher order statistics improves the detector performance.