Mutual information algorithms

Three new mutual information algorithms are raised for time delay in the phase space reconstruction process. Firstly, Cellucci's mutual information algorithm is analyzed based on partitioning plane, which is constructed by a pair of Lorenz series with the same size, into four and sixteen grids with equal distribution probability in elements on each axis. Then three new mutual information algorithms are promoted based on the original probability matrix that shows the distribution of points corresponding to the data pairs of Lorenz series on the plane, the matrix excluding the last column and the last row of the original one as well as the proportionally revised matrix from the original one. Synchronously, an algorithm to compute the probability matrix is also advanced by sorting two series and replacing each numerical value with its order number in its own series so as to Judge the element in which data sets are located The optimal time delay of the three new mutual information algorithms as well as the computing time is also compared when series sizes are different. Finally, after reconstructing phase space with the optimal time delay, comparison between the maximal Lyapunov exponent calculated by Rosenstein's algorithm from time series and that gained by Jacobi matrix from Lorenz equation is used to confirm the validity of the new mutual information algorithms. The results show that Cellucci's mutual information algorithm will lead to wrong optimal time delay when series size is not a multiple of elements The three new algorithms, whose results are more steady when a large number of data pairs are used, can not only eliminate the default of Cellucci's algorithm but also is very speedy, and the time spent on calculations by three algorithms nearly enhances linearly with the increase in series size. Moreover, the algorithm using original probability distribution matrix is more accurate than the others when small size series are used, and is also faster than the others irrespective of how large the size of series is. Besides, the lesser error of the maximal Lyapunov exponents from the comparison shows that the three new mutual information algorithms are available and feasible. (C) 2010 Elsevier Ltd All rights reserved