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 directions maximizing or minimizing the variance ratio between the two classes. The present contribution proves that kurtosis 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.

EEG Signal Processing in MI-BCI Applications With Improved Covariance Matrix Estimators.

In brain-computer interfaces (BCIs), the typical models of the EEG observations usually lead to a poor estimation of the trial covariance matrices, given the high non-stationarity of the EEG sources. We propose the application of two techniques that significantly improve the accuracy of these estimations and can be combined with a wide range of motor imagery BCI (MI-BCI) methods. The first one scales the observations in such a way that implicitly normalizes the common temporal strength of the source activities. When the scaling applies independently to the trials of the observations, the procedure justifies and improves the classical preprocessing for the EEG data. In addition, when the scaling is instantaneous and independent for each sample, the procedure particularizes to Tyler's method in statistics for obtaining a distribution-free estimate of scattering. In this case, the proposal provides an original interpretation of this existing method as a technique that pursuits an implicit instantaneous power-normalization of the underlying source processes. The second technique applies to the classifier and improves its performance through a convenient regularization of the features covariance matrix. Experimental tests reveal that a combination of the proposed techniques with the state-of-the-art algorithms for motor-imagery classification provides a significant improvement in the classification results.

Centroid-Based Clustering with αß-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 α ß -divergences, which is governed by two parameters, α and ß . We propose a new iterative algorithm, α ß -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 ( α , ß ). Our theoretical contribution has been validated by several experiments performed with synthetic and real data and exploring the ( α , ß ) plane. The numerical results obtained confirm the quality of the algorithm and its suitability to be used in several practical applications.

Information Theory Applications in Signal Processing.

The birth of Information Theory, right after the pioneering work of Claude Shannon and his celebrated publication of the paper "A mathematical theory of Communication" [...].

Information Theoretic Approaches for Motor-Imagery BCI Systems: Review and Experimental Comparison.

Brain computer interfaces (BCIs) have been attracting a great interest in recent years. The common spatial patterns (CSP) technique is a well-established approach to the spatial filtering of the electroencephalogram (EEG) data in BCI applications. Even though CSP was originally proposed from a heuristic viewpoint, it can be also built on very strong foundations using information theory. This paper reviews the relationship between CSP and several information-theoretic approaches, including the Kullback-Leibler divergence, the Beta divergence and the Alpha-Beta log-det (AB-LD)divergence. We also revise other approaches based on the idea of selecting those features that are maximally informative about the class labels. The performance of all the methods will be also compared via experiments.

The minimum risk principle that underlies the criteria of bounded component analysis.

This paper studies the problem of the blind extraction of a subset of bounded component signals from the observations of a linear mixture. In the first part of this paper, we analyze the geometric assumptions of the observations that characterize the problem, and their implications on the mixing matrix and latent sources. In the second part, we solve the problem by adopting the principle of minimizing the risk, which refers to the encoding complexity of the observations in the worst admissible situation. This principle provides an underlying justification of several bounded component analysis (BCA) criteria, including the minimum normalized volume criterion of the estimated sources or the maximum negentropy-likelihood criterion with a uniform reference model for the estimated sources. This unifying framework can explain the differences between the criteria in accordance with their considered hypotheses for the model of the observations. This paper is first presented for the case of the extraction of a complex and multidimensional source, and later is particularized for the case of the extraction of subsets of 1-D complex sources. The results also hold true in the case of real signals, where the obtained criteria for the extraction of a set of 1-D sources usually coincide with the existing BCA criteria.

Solving permutations in frequency-domain for blind separation of an arbitrary number of speech sources.

Blind separation of speech sources in reverberant environments is usually performed in the time-frequency domain, which gives rise to the permutation problem: the different ordering of estimated sources for different frequency components. A two-stage method to solve permutations with an arbitrary number of sources is proposed. The suggested procedure is based on the spectral consistency of the sources. At the first stage frequency bins are compared with each other, while at the second stage the neighboring frequencies are emphasized. Experiments for perfect separation situations and for live recordings show that the proposed method improves the results of existing approaches.

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

This article addresses the problem of the unsupervised separation 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 solutions in that domain and helps to reduce the execution time of the algorithms. Simulations confirm these advantages for several ICA instantaneous algorithms and the effectiveness of the proposed technique in emulated reverberant environments.