基于核函数的混沌序列局域线性预测方法

Novel local linear predictor of chaotic time series based on kernel function

针对局域线性预测方法本质上是用较简单的非线性函数来预测高度非线性的混沌时间序列的不足,提出了一种基于核函数的局域线性自适应预测算法。该算法利用包含了相空间中邻近点之间的相对距离信息的核函数,将相空间中的邻近点投影到更高维的非线性核空间,在高维(甚至无穷维)的核空间用线性自适应算法预测混沌时间序列,相当于在原混沌相空间用高度非线性的函数预测高度非线性的混沌时间序列,可获得更好的预测结果。给出了应用该方法的具体步骤,通过仿真实验证明了该算法的有效性。

Aiming at the disadvantage that the local linear predictor estimates the high complicated nonlinear chaotic time series by the simple nonlinear function, a novel local linear prediction method based on the kernel function is presented. The proposed algorithm projects the points in the phase space into the higher-dimension kernel space by the kernel function, and estimates the chaotic time series in the higher dimension kernel space by an adaptive predictor. The proposed method is equivalent to estimate high-complicated nonlinear chaotic series by high-complicated nonlinear function in the origin phase space, and can predict chaotic sequence more exactly. The experiment shows that the proposed method is effective.