Kernel Feature Extraction in Signal Processing - Rojo-Álvarez, José Luis; Martínez-Ramón, Manel; Muñoz-Mar&iacute, Jordi; Camps-Valls, Gustau (Digital Signal Processing with Kernel Methods, 2018)
Kernel‐based feature extraction and dimensionality reduction are becoming increasingly important in advanced signal processing. This is particularly relevant in applications dealing with very high‐dimensional data. Besides changing the data representation space via kernel feature extraction, another possibility is to correct for biases in the data distributions operating on the samples. This chapter reviews the main kernel feature extraction and dimensionality reduction methods, dealing with supervised, unsupervised and semi‐supervised settings. It illustrates methods in toy examples, as well as real datasets. The chapter also analyzes the connections between Hilbert‐Schmidt independence criterion (HSIC) and classical feature extraction methods. The HSIC method measures cross‐covariance in an adequate reproducing kernel Hilbert space (RKHS) by using the entire spectrum of the cross‐covariance operator. Kernel dimensionality reduction (KDR) is a supervised feature extraction method that seeks a linear transformation of the data such that it maximizes the conditional HSIC on the labels.