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6. A Unified SVM Framework for Signal Estimation

Author

Rojo-Álvarez, José Luis, Martínez-Ramón, Manel, Muñoz-Marí, Jordi, and Camps-Valls, Gustavo

Subjects
Statistics - Machine Learning, Statistics - Applications
Abstract

This paper presents a unified framework to tackle estimation problems in Digital Signal Processing (DSP) using Support Vector Machines (SVMs). The use of SVMs in estimation problems has been traditionally limited to its mere use as a black-box model. Noting such limitations in the literature, we take advantage of several properties of Mercer's kernels and functional analysis to develop a family of SVM methods for estimation in DSP. Three types of signal model equations are analyzed. First, when a specific time-signal structure is assumed to model the underlying system that generated the data, the linear signal model (so called Primal Signal Model formulation) is first stated and analyzed. Then, non-linear versions of the signal structure can be readily developed by following two different approaches. On the one hand, the signal model equation is written in reproducing kernel Hilbert spaces (RKHS) using the well-known RKHS Signal Model formulation, and Mercer's kernels are readily used in SVM non-linear algorithms. On the other hand, in the alternative and not so common Dual Signal Model formulation, a signal expansion is made by using an auxiliary signal model equation given by a non-linear regression of each time instant in the observed time series. These building blocks can be used to generate different novel SVM-based methods for problems of signal estimation, and we deal with several of the most important ones in DSP. We illustrate the usefulness of this methodology by defining SVM algorithms for linear and non-linear system identification, spectral analysis, nonuniform interpolation, sparse deconvolution, and array processing. The performance of the developed SVM methods is compared to standard approaches in all these settings. The experimental results illustrate the generality, simplicity, and capabilities of the proposed SVM framework for DSP., Comment: 22 pages, 13 figures. Digital Signal Processing, 2014

Published
2013

19. Prognostic Significance of Long-Period Heart Rate Rhythms in Chronic Heart Failure

Author

Pastor-Pérez, Francisco J., primary, Manzano-Fernández, Sergio, additional, Goya-Esteban, Rebeca, additional, Pascual-Figal, Domingo A., additional, Barquero-Pérez, Oscar, additional, Rojo-Álvarez, Jose Luis, additional, Everss, Estrella, additional, Martinez Martinez-Espejo, Maria Dolores, additional, Valdés Chavarri, Mariano, additional, and García-Alberola, Arcadi, additional

Published
2012
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20. Kernel Antenna Array Processing.

Author

Martínez-Ramón, Manel, Rojo-Álvarez, Jose Luis, Camps-Valls, Gustavo, and Christodoulou, Christos G.

Subjects
*ANTENNAS (Electronics), *VECTOR analysis, *MAXIMA & minima, *SIGNAL-to-noise ratio, *ANTENNA arrays
Abstract

We introduce two support vector machine (SVM)-based approaches for solving antenna problems such as beamforming, sidelobe suppression, and maximization of the signal-to-noise ratio. A basic introduction to SVM optimization is provided and a complex nonlinear SVM formulation developed to handle antenna array processing in space and time. The new optimization formulation is compared with both the minimum mean square error and the minimum variance distortionless response methods. Several examples are included to show the performance of the new approaches [ABSTRACT FROM PUBLISHER]

Published
2007
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