  In most adaptive signal processing applications, system linearity is assumed
and adaptive linear filters are thus used. The traditional class of supervised
adaptive filters rely on error-correction learning for their adaptive
capability. The kernel method is a powerful nonparametric modeling tool for
pattern analysis and statistical signal processing. Through a nonlinear
mapping, kernel methods transform the data into a set of points in a
Reproducing Kernel Hilbert Space. KRLS achieves high accuracy and has fast
convergence rate in stationary scenario. However the good performance is
obtained at a cost of high computation complexity. Sparsification in kernel
methods is know to related to less computational complexity and memory
consumption.
