Digital Signal Processing with Kernel Methods

3Signal Processing Models

3.1 Introduction

Classical taxonomies on signal processing and analysis often distinguish between estimation and detection problems, which are often known in machine learning as regression and classification respectively. Up to four main data models in statistical Learning were pointed out further by Cherkassky and Mulier (1998); namely, clustering, density estimation, classification, and regression. Models in these paradigms can be adjusted (tuned, trimmed, fitted) to the available datasets by following different inductive principles, including MMSE and ML criteria. On the other hand, time series analysis has provided a wide variety of paradigms for parametric modeling to be adjusted in terms of their time properties, which can be summarized in the autocorrelation and cross‐correlation statistical descriptions. The good news with SVM and kernel methods is that they provide at least two main advantageous elements, such as the kernel trick and the single solution inductive principle. These advantages allowed the kernel methods community to revisit old, well‐established data models successfully. However, the existing richness of data models in time series analysis, statistics, and many other data processing fields has not always been taken into account, so there is still room for improving experimental performance and more solid theoretical analysis.

Signal estimation, regression, and function approximation are old, largely studied problems in signal ...