Random fourier feature kernel recursive least squares

Abstract

In this paper, we investigate the nonlinear, finite dimensional and data independent random Fourier feature expansions that can approximate the popular Gaussian kernel. With recursive least squares algorithm, we develop the Random Fourier Feature Recursive Least Squares algorithm (RFF-RLS), which shows significant performance improvements in simulations when compared with several other online kernel learning algorithms such as Kernel Least Mean Square (KLMS) and Kerne Recursive Least Squares (KRLS). Our results confirm that the RFF-RLS can achieve desirable performance with low computational cost. As for the random Fourier features, the randomization generally results in redundancy. We use an algorithm, namely, Vector Quantization with Information Theoretic Learning (VQIT) to decrease the dictionary size. The resulting sparse dictionary can match the original data distribution well. The RFF-RLS with VQIT can outperform the RFF-RLS without VQIT.