The Research Of Kernel Adaptive Filtering Algorithm Based On Maximum Correntropy Criterion

Kernel adaptive filtering(KAF) algorithms, a bunch of effective learning methods for nonlinear system, have been widely used in a variety of applications such as system identification, channel equalization, acoustic echo cancellation, and so on. In most cases, additive noises in signal processing are always supposed as Gaussian Process, thus mean square error(MSE) is always adopted in the construction of kernel adaptive filtering algorithms. However, in the real world, signals in many physical phenomena show non-Gaussian behaviors, such as underwater noise, atmospheric noise and so on. In the past ten years, Information Theoretic Learning(ITL) has made great progress, and has been widely used in non-Gaussian signal processing. In ITL, correntropy measures a novel localized similarity between two random variables, which, compared to MSE, captures more statistic information from data. Therefore, algorithms based on correntropy show robustness against non-Gaussian noises.In this paper, a novel kernel adaptive filtering algorithm is proposed, which is based on kernel recursive least squares(KRLS) and correntropy. Its performance is analyzed in chaotic time series prediction simulations. The research works of this paper are showed in two parts.Firstly, by introducing correntropy, kernel recursive algorithm based on maximum correntropy criterion(MCC), called kernel recursive maximum correntropy(KRMC), is proposed. Kernel method transforms data from input data space to feature space, in which linear adaptive filtering algorithm is applied to adjust the weights of adaptive filter. The KRMC algorithm updates equation recursively by maximizing the correntropy between output of the system and the desired signal. Compared to KRLS, the KRMC algorithm suppress the bad effects of impulsive noise through kernel function in correntropy, thus guarantees a good performance for non-Gaussian application. MSE performance is analyzed in chaotic time series prediction simulation. The effect of kernel width in correntropy on the KRMC algorithm is also analyzed.Secondly, quantized KRMC(QKRMC) is proposed to deal with the problem that network architecture of KRMC is linear growing with iteration. The QKRMC algorithm initializes an empty dictionary in the beginning, and records the qualified input data as a new center with every iteration. Network architecture of the QKRMC algorithm is controlled by quantization threshold, which balances the network architecture with MSE performance. MSE performance is analyzed in chaotic time series prediction simulation. The effect of quantization threshold on the QKRMC algorithm is also analyzed.