How to estimate the correlation dimension of high-dimensional signals?

The paper presents improvements to the Takens-Ellner (TE) algorithm estimating the correlation dimension (d) of high-dimensional signals. The signal being the sum of 4 Lorenz signals and possessing the correlation dimension d approximately equal to 8 was analyzed. The conversion of TE to the classic Grassberger-Proccacia (GP) algorithm is presented that shows the advantage of TE over the GP algorithm. The maximal d estimated for the given number of points in phase space is significantly higher for the TE algorithm than for the GP algorithm. The formula for the precision of individual d estimation is presented. The paper shows, how to estimate the distance corresponding to the end of the Linear Scaling Region in the correlation integral function, even before starting the procedure of d estimation. It makes it possible to reject the majority of longer distances from the analysis reducing the computation time considerably.

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