Kernel generalized affine projection-like algorithms for time-series prediction

In reproducing kernel Hilbert space, a novel kernel adaptive filtering algorithm, named kernel generalized affine projection-like algorithm (K-GAPLA), is derived. The cost function is optimized by using the mixed-norm and generalized correntropy methods for the proposed K-GAPLA, which can be treated as an extension of kernel affine projection-like algorithm (APLA) that is based on a correntropy approach. What's more, applying the kernel trick and leaky way to generalized APLA (GAPLA) yields a new kernel leaky GAPLA (KL-GAPLA) in order to improve the performance of K-GAPLA. Furthermore, the variable step-size (VSS) and modified VSS (MVSS) ways are incorporated into KL-GAPLA resulting in VSS-KL-GAPLA and MVSS-KL-GAPLA, respectively. Simulations verify that the proposed kernel algorithms outperform other known kernel affine projection-type algorithms in the context of time-series prediction.