Prediction of chaotic time series based on Nystrom Cauchy kernel conjugate gradient algorithm

Chaotic time series can well reflect the nonlinearity and non-stationarity of real environment changes. The traditional kernel adaptive filter (KAF) with second-order statistical characteristics suffers performance degeneration dramatically for predicting chaotic containing noises outliers. In order to improve robustness filters in presence impulsive noise, a nonlinear similarity measure named Cauchy loss (CKL) is proposed, global convexity CKL guaranteed by half-quadratic (HQ) method. To convergence rate stochastic gradient descent avoid local optimum simultaneously, conjugate (CG) method used optimize CKL. Furthermore, address issue matrix network growth, Nyström sparse strategy adopted approximate then probability density rank-based quantization (PRQ) approximation accuracy. this end, novel PRQ (NCKCG-PRQ) algorithm proposed prediction paper. Simulations on synthetic real-world validate advantages terms filtering accuracy, robustness, computational storage complexity.