arXiv subjects
Publications and source records attributed to Alain Rakotomamonjy.
The objectives of this technical report is to provide additional results on the generalized conditional gradient methods introduced by Bredies et al. [BLM05]. Indeed , when the objective function is smooth, we provide a novel certificate of optimality and we show that the algorithm has a linear convergence rate. Applications of this algorithm are also discussed.
This paper addresses the problem of audio scenes classification and contributes to the state of the art by proposing a novel feature. We build this feature by considering histogram of gradients (HOG) of time-frequency representation of an audio scene. Contrarily to classical audio features like MFCC, we make the hypothesis that histogram of gradients are able to encode some relevant informations in a time-frequency {representation:} namely, the local direction of variation (in time and frequency) of the signal spectral power. In addition, in order to gain more invariance and robustness, histogram of gradients are locally pooled. We have evaluated the relevance of {the novel feature} by comparing its performances with state-of-the-art competitors, on several datasets, including a novel one that we provide, as part of our contribution. This dataset, that we make publicly available, involves $19$ classes and contains about $900$ minutes of audio scene recording. We thus believe that it may be the next standard dataset for evaluating audio scene classification algorithms. Our comparison results clearly show that our HOG-based features outperform its competitors
We introduce a novel algorithm for solving learning problems where both the loss function and the regularizer are non-convex but belong to the class of difference of convex (DC) functions. Our contribution is a new general purpose proximal Newton algorithm that is able to deal with such a situation. The algorithm consists in obtaining a descent direction from an approximation of the loss function and then in performing a line search to ensure sufficient descent. A theoretical analysis is provided showing that the iterates of the proposed algorithm {admit} as limit points stationary points of the DC objective function. Numerical experiments show that our approach is more efficient than current state of the art for a problem with a convex loss functions and non-convex regularizer. We have also illustrated the benefit of our algorithm in high-dimensional transductive learning problem where both loss function and regularizers are non-convex.
This work investigates the use of mixed-norm regularization for sensor selection in Event-Related Potential (ERP) based Brain-Computer Interfaces (BCI). The classification problem is cast as a discriminative optimization framework where sensor selection is induced through the use of mixed-norms. This framework is extended to the multi-task learning situation where several similar classification tasks related to different subjects are learned simultaneously. In this case, multi-task learning helps in leveraging data scarcity issue yielding to more robust classifiers. For this purpose, we have introduced a regularizer that induces both sensor selection and classifier similarities. The different regularization approaches are compared on three ERP datasets showing the interest of mixed-norm regularization in terms of sensor selection. The multi-task approaches are evaluated when a small number of learning examples are available yielding to significant performance improvements especially for subjects performing poorly.
Although operator-valued kernels have recently received increasing interest in various machine learning and functional data analysis problems such as multi-task learning or functional regression, little attention has been paid to the understanding of their associated feature spaces. In this paper, we explore the potential of adopting an operator-valued kernel feature space perspective for the analysis of functional data. We then extend the Regularized Least Squares Classification (RLSC) algorithm to cover situations where there are multiple functions per observation. Experiments on a sound recognition problem show that the proposed method outperforms the classical RLSC algorithm.
In this paper, we address the problem of embedded feature selection for ranking on top of the list problems. We pose this problem as a regularized empirical risk minimization with $p$-norm push loss function ($p=\infty$) and sparsity inducing regularizers. We leverage the issues related to this challenging optimization problem by considering an alternating direction method of multipliers algorithm which is built upon proximal operators of the loss function and the regularizer. Our main technical contribution is thus to provide a numerical scheme for computing the infinite push loss function proximal operator. Experimental results on toy, DNA microarray and BCI problems show how our novel algorithm compares favorably to competitors for ranking on top while using fewer variables in the scoring function.
In this paper, we formulate the Canonical Correlation Analysis (CCA) problem on matrix manifolds. This framework provides a natural way for dealing with matrix constraints and tools for building efficient algorithms even in an adaptive setting. Finally, an adaptive CCA algorithm is proposed and applied to a change detection problem in EEG signals.
Positive definite operator-valued kernels generalize the well-known notion of reproducing kernels, and are naturally adapted to multi-output learning situations. This paper addresses the problem of learning a finite linear combination of infinite-dimensional operator-valued kernels which are suitable for extending functional data analysis methods to nonlinear contexts. We study this problem in the case of kernel ridge regression for functional responses with an lr-norm constraint on the combination coefficients. The resulting optimization problem is more involved than those of multiple scalar-valued kernel learning since operator-valued kernels pose more technical and theoretical issues. We propose a multiple operator-valued kernel learning algorithm based on solving a system of linear operator equations by using a block coordinatedescent procedure. We experimentally validate our approach on a functional regression task in the context of finger movement prediction in brain-computer interfaces.
One of the major challenges of ECoG-based Brain-Machine Interfaces is the movement prediction of a human subject. Several methods exist to predict an arm 2-D trajectory. The fourth BCI Competition gives a dataset in which the aim is to predict individual finger movements (5-D trajectory). The difficulty lies in the fact that there is no simple relation between ECoG signals and finger movement. We propose in this paper to decode finger flexions using switching models. This method permits to simplify the system as it is now described as an ensemble of linear models depending on an internal state. We show that an interesting accuracy prediction can be obtained by such a model.
Signal Sequence Labeling consists in predicting a sequence of labels given an observed sequence of samples. A naive way is to filter the signal in order to reduce the noise and to apply a classification algorithm on the filtered samples. We propose in this paper to jointly learn the filter with the classifier leading to a large margin filtering for classification. This method allows to learn the optimal cutoff frequency and phase of the filter that may be different from zero. Two methods are proposed and tested on a toy dataset and on a real life BCI dataset from BCI Competition III.
We address in this paper the problem of multi-channel signal sequence labeling. In particular, we consider the problem where the signals are contaminated by noise or may present some dephasing with respect to their labels. For that, we propose to jointly learn a SVM sample classifier with a temporal filtering of the channels. This will lead to a large margin filtering that is adapted to the specificity of each channel (noise and time-lag). We derive algorithms to solve the optimization problem and we discuss different filter regularizations for automated scaling or selection of channels. Our approach is tested on a non-linear toy example and on a BCI dataset. Results show that the classification performance on these problems can be improved by learning a large margin filtering.
This paper reviews the functional aspects of statistical learning theory. The main point under consideration is the nature of the hypothesis set when no prior information is available but data. Within this framework we first discuss about the hypothesis set: it is a vectorial space, it is a set of pointwise defined functions, and the evaluation functional on this set is a continuous mapping. Based on these principles an original theory is developed generalizing the notion of reproduction kernel Hilbert space to non hilbertian sets. Then it is shown that the hypothesis set of any learning machine has to be a generalized reproducing set. Therefore, thanks to a general "representer theorem", the solution of the learning problem is still a linear combination of a kernel. Furthermore, a way to design these kernels is given. To illustrate this framework some examples of such reproducing sets and kernels are given.