Discrete Time Signal Processing Framework with Support Vector Machines
José Luis Rojo-Álvarez (Universidad Rey Juan Carlos, Spain), Manel Martínez-Ramón (Universidad Carlos III de Madrid, Spain), Gustavo Camps-Valls (Universitat de València, Spain), Carlos E. Martínez-Cruz (Universidad Carlos III de Madrid, Spain) and Carlos Figuera (Universidad Rey Juan Carlos, Spain)
Copyright: © 2007
Digital signal processing (DSP) of time series using SVM has been addressed in the literature with a straightforward application of the SVM kernel regression, but the assumption of independently distributed samples in regression models is not fulfilled by a time-series problem. Therefore, a new branch of SVM algorithms has to be developed for the advantageous application of SVM concepts when we process data with underlying time-series structure. In this chapter, we summarize our past, present, and future proposal for the SVM-DSP frame-work, which consists of several principles for creating linear and nonlinear SVM algorithms devoted to DSP problems. First, the statement of linear signal models in the primal problem (primal signal models) allows us to obtain robust estimators of the model coefficients in classical DSP problems. Next, nonlinear SVM-DSP algorithms can be addressed from two different approaches: (a) reproducing kernel Hilbert spaces (RKHS) signal models, which state the signal model equation in the feature space, and (b) dual signal models, which are based on the nonlinear regression of the time instants with appropriate Mercer’s kernels. This way, concepts like filtering, time interpolation, and convolution are considered and analyzed, and they open the field for future development on signal processing algorithms following this SVM-DSP framework.