BCI competition III: dataset II- ensemble of SVMs for BCI P300 speller

Brain-computer interface P300 speller aims at helping patients unable to activate muscles to spell words by means of their brain signal activities. Associated to this BCI paradigm, there is the problem of classifying electroencephalogram signals related to responses to some visual stimuli. This paper addresses the problem of signal responses variability within a single subject in such brain-computer interface. We propose a method that copes with such variabilities through an ensemble of classifiers approach. Each classifier is composed of a linear support vector machine trained on a small part of the available data and for which a channel selection procedure has been performed. Performances of our algorithm have been evaluated on dataset II of the BCI Competition III and has yielded the best performance of the competition.     

Wavelet kernel learning

This paper addresses the problem of optimal feature extraction from a wavelet representation. Our work aims at building features by selecting wavelet coefficients resulting from signal or image decomposition on an adapted wavelet basis. For this purpose, we jointly learn in a kernelized large-margin context the wavelet shape as well as the appropriate scale and translation of the wavelets, hence the name “wavelet kernel learning”. This problem is posed as a multiple kernel learning problem, where the number of kernels can be very large. For solving such a problem, we introduce a novel multiple kernel learning algorithm based on active constraints methods. We furthermore propose some variants of this algorithm that can produce approximate solutions more efficiently. Empirical analysis show that our active constraint MKL algorithm achieves state-of-the art efficiency. When used for wavelet kernel learning, our experimental results show that the approaches we propose are competitive with respect to the state-of-the-art on brain–computer interface and Brodatz texture datasets.     

Longitudinal modelling and control of a flapping-wing micro aerial vehicle

A simulation model, flight-dynamics oriented, of a flapping-wing micro aerial vehicle (MAV) is presented here. The model, based on animal flapping flight, integrates the aerodynamic forces computed along each wing to determine the global motion of the MAV with respect to an inertial reference frame. After some analytic simplifications, and taking into account the periodic nature of the system inputs, an averaged model is derived, and a simple, nonlinear closed-loop control law is designed for the dynamics along the vertical and pitch axis, allowing an efficient stabilization of the naturally unstable model.     

Surveying and comparing simultaneous sparse approximation (or group-lasso) algorithms

In this paper, we survey and compare different algorithms that, given an overcomplete dictionary of elementary functions, solve the problem of simultaneous sparse signal approximation, with common sparsity profile induced by a ?_p−?_q mixed-norm. Such a problem is also known in the statistical learning community as the group lasso problem. We have gathered and detailed different algorithmic results concerning these two equivalent approximation problems. We have also enriched the discussion by providing relations between several algorithms. Experimental comparisons of the detailed algorithms have also been carried out. The main lesson learned from these experiments is that depending on the performance measure, greedy approaches and iterative reweighted algorithms are the most efficient algorithms either in term of computational complexities, sparsity recovery or mean-square error.     

Composite kernel learning

The Support Vector Machine is an acknowledged powerful tool for building classifiers, but it lacks flexibility, in the sense that the kernel is chosen prior to learning. Multiple Kernel Learning enables to learn the kernel, from an ensemble of basis kernels, whose combination is optimized in the learning process. Here, we propose Composite Kernel Learning to address the situation where distinct components give rise to a group structure among kernels. Our formulation of the learning problem encompasses several setups, putting more or less emphasis on the group structure. We characterize the convexity of the learning problem, and provide a general wrapper algorithm for computing solutions. Finally, we illustrate the behavior of our method on multi-channel data where groups correspond to channels.     

Learning with infinitely many features

We propose a principled framework for learning with infinitely many features, situations that are usually induced by continuously parametrized feature extraction methods. Such cases occur for instance when considering Gabor-based features in computer vision problems or when dealing with Fourier features for kernel approximations. We cast the problem as the one of finding a finite subset of features that minimizes a regularized empirical risk. After having analyzed the optimality conditions of such a problem, we propose a simple algorithm which has the flavour of a column-generation technique. We also show that using Fourier-based features, it is possible to perform approximate infinite kernel learning. Our experimental results on several datasets show the benefits of the proposed approach in several situations including texture classification and large-scale kernelized problems (involving about 100 thousand examples).     

Wasserstein discriminant analysis

Wasserstein discriminant analysis (WDA) is a new supervised linear dimensionality reduction algorithm. Following the blueprint of classical Fisher Discriminant Analysis, WDA selects the projection matrix that maximizes the ratio of the dispersion of projected points pertaining to different classes and the dispersion of projected points belonging to a same class. To quantify dispersion, WDA uses regularized Wasserstein distances. Thanks to the underlying principles of optimal transport, WDA is able to capture both global (at distribution scale) and local (at samples’ scale) interactions between classes. In addition, we show that WDA leverages a mechanism that induces neighborhood preservation. Regularized Wasserstein distances can be computed using the Sinkhorn matrix scaling algorithm; the optimization problem of WDA can be tackled using automatic differentiation of Sinkhorn’s fixed-point iterations. Numerical experiments show promising results both in terms of prediction and visualization on toy examples and real datasets such as MNIST and on deep features obtained from a subset of the Caltech dataset.