Support vector machines framework for linear signal processing

This paper presents a support vector machines (SVM) framework to deal with linear signal processing (LSP) problems. The approach relies on three basic steps for model building: (1) identifying the suitable base of the Hilbert signal space in the model, (2) using a robust cost function, and (3) minimizing a constrained, regularized functional by means of the method of Lagrange multipliers. Recently, autoregressive moving average (ARMA) system identification and non-parametric spectral analysis have been formulated under this framework. The generalized, yet simple, formulation of SVM LSP problems is particularized here for three different issues: parametric spectral estimation, stability of Infinite Impulse Response filters using the gamma structure, and complex ARMA models for communication applications. The good performance shown on these different domains suggests that other signal processing problems can be stated from this SVM framework.Publicad

Robust ASR using Support Vector Machines

The improved theoretical properties of Support Vector Machines with respect to other machine learning alternatives due to their max-margin training paradigm have led us to suggest them as a good technique for robust speech recognition. However, important shortcomings have had to be circumvented, the most important being the normalisation of the time duration of different realisations of the acoustic speech units. In this paper, we have compared two approaches in noisy environments: first, a hybrid HMM–SVM solution where a fixed number of frames is selected by means of an HMM segmentation and second, a normalisation kernel called Dynamic Time Alignment Kernel (DTAK) first introduced in Shimodaira et al. [Shimodaira, H., Noma, K., Nakai, M., Sagayama, S., 2001. Support vector machine with dynamic time-alignment kernel for speech recognition. In: Proc. Eurospeech, Aalborg, Denmark, pp. 1841–1844] and based on DTW (Dynamic Time Warping). Special attention has been paid to the adaptation of both alternatives to noisy environments, comparing two types of parameterisations and performing suitable feature normalisation operations. The results show that the DTA Kernel provides important advantages over the baseline HMM system in medium to bad noise conditions, also outperforming the results of the hybrid system.Publicad

Analyzing sparse dictionaries for online learning with kernels

Many signal processing and machine learning methods share essentially the same linear-in-the-parameter model, with as many parameters as available samples as in kernel-based machines. Sparse approximation is essential in many disciplines, with new challenges emerging in online learning with kernels. To this end, several sparsity measures have been proposed in the literature to quantify sparse dictionaries and constructing relevant ones, the most prolific ones being the distance, the approximation, the coherence and the Babel measures. In this paper, we analyze sparse dictionaries based on these measures. By conducting an eigenvalue analysis, we show that these sparsity measures share many properties, including the linear independence condition and inducing a well-posed optimization problem. Furthermore, we prove that there exists a quasi-isometry between the parameter (i.e., dual) space and the dictionary's induced feature space.Comment: 10 page