A Unified SVM Framework for Signal Estimation

This paper presents a review in the form of a unified framework for tackling estimation problems in Digital Signal Processing (DSP) using Support Vector Machines (SVMs). The paper formalizes our developments in the area of DSP with SVM principles. The use of SVMs for DSP is already mature, and has gained popularity in recent years due to its advantages over other methods: SVMs are flexible non-linear methods that are intrinsically regularized and work well in low-sample-sized and high-dimensional problems. SVMs can be designed to take into account different noise sources in the formulation and to fuse heterogeneous information sources. Nevertheless, 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