Quantized kernel recursive minimum error entropy algorithm

Abstract

In this paper, we propose a online vector quantization (VQ) method based on the kernel recursive minimum error entropy (KRMEE) algorithm. According to information theoretic learning (ITL), the minimum error entropy criterion (MEE) is robust and can effective resistance to non-Gaussian noise. By combining the kernel recursive least squares (KRLS) algorithm with MEE criterion, KRMEE algorithm has been generated, which has excellent performance in non-Gaussian environments. However, with the size of data increases, the computational complexity will raise. We propose a quantized to solve this problem, the input space of the algorithm is quantized to suppress the linear growth radial basis function (RBF) network in kernel adaptive filtering (KAF). The VQ method is different from novelty criterion (NC), approximate linear dependency (ALD) criterion, and other sparsity methods, the online VQ method need to construct the dictionary, and calculate the distance by Euclidean norm. We propose a novel quantized kernel recursive minimum error entropy (QKRMEE) algorithm by combining VQ method with KRMEE algorithm, and update the solution with a recursive algorithm. In Mackey-Glass time series and a real-world datasets, Monte Carlo simulation experiments show that the proposed algorithm achieves better predictive performance in non-Gaussian noise environment. Meanwhile, the algorithm can restrain the growth of RBF network well, thus reducing the computational complexity and memory consumption effectively.