基于改进典型相关分析的混沌时间序列预测

典型相关分析是目前常用的研究两个变量集间相关性的统计方法.针对线性典型相关分析法不能揭示变量间非线性关系,因而不适用于混沌系统等问题,将核典型相关分析与径向基函数神经网络相结合,提出了一种改进的核典型相关分析方法以解决映射空间样本未知及逆矩阵求解困难等问题.首先利用两个径向基函数神经网络,通过训练使两个网络输出之间的相关系数达到最大,可同时得到两组典型相关变量.然后建立预测模型,对Lorenz混沌方程及大连月气温与降雨二变量混沌时间序列进行仿真,并与传统的线性回归预测方法进行比较,多组仿真结果证明了所述方法的有效性.

Chaotic time series prediction based on modified canonical correlation analysis

Canonical correlation analysis (CCA) is a common statistical method to study the correlativity between two sets of variables. Linear CCA cannot reveal the underlying nonlinear relationship between variables, so it is not suitable for the chaotic systems. Kernel CCA (KCCA) is a useful method to improve such a linear method. A new nonlinear CCA method based on KCCA and radial basis function (RBF) neural network is proposed to solve the problem of the complexity of computation and overcome the difficulty of computing the inverse matrix. To obtain the canonical variables, two RBF networks are trained to maximize their correlation coefficient, and then a prediction model is constructed. Simulations are conducted on Lorenz system, the monthly temperature and rainfall of Dalian. Comparison results with the existing linear regression (LR) method show that the proposed method is effective.