四阶累积量用于最小嵌入维数估计的新方法

用能反映非线性结构的四阶累积量函数代替相关函数构造矩阵,对奇异值分解法进行改进.对比分析了用四阶累积量函数构造矩阵的多种方法,得到两种较好的构造矩阵的方法.其中当四阶累积量函数的两个变量分别在矩阵的对角线方向和偏离对角线方向取值并且第三个变量取零时,得到的矩阵的分析效果最好.并用此方法分析由Henon映射、Lorenz模型生成的混沌时间序列.实验结果表明了改进后方法的有效性及稳定性,并且改进后方法适合小数据量的情况且计算效率高.

New Method for Determining the Minimum Embedding Dimension Based on Four-order Cumulant

Singular value decomposition is essentially a linear method based on the covariance matrix which reflects the linear dependence. Numerical experience led several researchers to express some doubts about the reliability of SVD. In this paper the matrix constructed by four-order cumulant function instead of correlation function is used to improve the method of SVD. Methods used four-order cumulant function to construct matrixes is studied and the best two methods are found. When two parameters of four-order cumulant function choose values of the diagonal direction and the off-diagonal direction of the matrix and the third parameter is zero, we can get the best matrix. In this paper we illustrate this method to analyze chaotic time series from Henon attractor and Lorenz model. Simulation results show the validity and the stability of the improved method. And this method is fit for the small set nonlinear time series and is computationally efficient.