Adaptive Kernel Learning for Signal Processing - Rojo-Álvarez, José Luis; Martínez-Ramón, Manel; Muñoz-Mar&iacute, Jordi; Camps-Valls, Gustau (Digital Signal Processing with Kernel Methods, 2018)
Adaptive filtering is a central topic in digital signal processing (DSP). By applying linear adaptive filtering principles in the kernel feature space, powerful nonlinear adaptive filtering algorithms can be obtained. This chapter introduces the wide topic of adaptive signal processing, and explores the emerging field of kernel adaptive filtering (KAF). In many signal processing applications, the problem of signal estimation is addressed. Probabilistic models have proven to be very useful in this context. The chapter discusses two families of kernel adaptive filters, namely kernel least mean squares (KLMS) and kernel recursive least‐squares (KRLS) algorithms. In order to design a practical KLMS algorithm, the number of terms in the kernel expansion in given equation should stop growing over time. This can be achieved by implementing an online sparsification technique, whose aim is to identify terms in the kernel expansion that can be omitted without degrading the solution. The chapter also discusses several different sparsification approaches.