New Method for Determining the Minimum Embedding Dimension Based on Four-order Cumulant
四阶累积量用于最小嵌入维数估计的新方法

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.