Kernel fractional affine projection algorithm
Kernel-based learning algorithms gained interest since the last few years. Mercer's theorem is used in kernel-based learning algorithms to map the input data using some nonlinear kernel function to some higher dimensional feature space, known as reproducing kernel Hilbert space (RKHS), where the linear operations are easily performed on the input data. These kernel methods stem originally from support vector machines (Vapnik and Vapnik 1998; Hearst et al. 1998 ), a powerful tool in handling
... sification problems in the neural network architecture. Kernel principal component analysis (KPCA) and kernel regression (Scholkopf et al. 1997; Takeda et al. 2007; Hardle and Vieu 1992) also show desirable performance regarding classification in the complicated environment of statistical signal processing. However, these are batch mode methods and suffer the burden of high computational cost and memory usage. These issues are replaced by introducing the online kernel methods, such as kernel least mean square (KLMS) (Liu et al. 2008), kernel affine projection algorithm (KAPA) (Liu and Principe 2008), kernel recursive least squares (KRLS) (Engel et al. 2004; Liu et al. 2015) and extended kernel recursive least squares (Ex-KRLS) (Liu et al. 2009) algorithms. These online kernel algorithms are very much in common nowadays regarding system identification, weather forecasting, nonlinear channel equalization, prediction of stationary as well as nonstationary time Abstract This paper extends the kernel affine projection algorithm to a rich, flexible and cohesive taxonomy of fractional signal processing approach. The formulation of the algorithm is established on the inclusion of Riemann-Liouville fractional derivative to gradient-based stochastic Newton recursive method to minimize the cost function of the kernel affine projection algorithm. This approach extends the idea of fractional signal processing in reproducing kernel Hilbert space. The proposed algorithm is applied to the prediction of chaotic Lorenz time series and nonlinear channel equalization. Also the performance is validated in comparison with the least mean square algorithm, kernel least mean square algorithm, affine projection algorithm and kernel affine projection algorithm.