Abstract
The paper describes the improvements and corrections to the method of estimation of correlation dimension of d for high-dimensional signals (HDS). The following problems are described: (a) presentation of the quick version of the algorithm that reduces computation time, (b) improvement of the precision of the elementary Takens-Ellner formula estimating d, (c) the problem of strongly non-gaussian signals and its possible normalisation. Appendix discusses the use of author’s Matlab function estimating d which is available for public use.
Highlights
SCHEDULE OF THE PAPERCurrent paper focuses on the following aspects of the algorithm: 1. Presenting new ideas improving and accelerating the algorithm
One of the important conclusions presented in Ref. 6 is the possibility to estimate the approximate end of plateau in d =fn(Pmax) relation based on the assumed deflection error e in the histogram convolution plot
The first step of Pmo ax and δmax estimation consists in the building of the histogram convolution plots up to the embedding dimension m used for the given W iteration
Summary
Current paper focuses on the following aspects of the algorithm: 1. Presenting new ideas improving and accelerating the algorithm. Current paper focuses on the following aspects of the algorithm: 1. Presenting new ideas improving and accelerating the algorithm. 2. Improving the precision of the elementary Takens-Ellner formula. 3. Defining and reduction of the problem of δ-vector reduction. 4. Presenting the problem of strongly non-Gaussian signals and showing some aspects connected with the preliminary normalization of the signal. 5. Presenting the example of the signal possessing 2 plateaus in the relation d =fn(W ). We present the use of the free available Matlab toolkit with the implementation of the algorithm. This chapter is dedicated for scientists who want use all the implemented options of the algorithm. The HDS-toolkit is available on author’s website “www.drmichalak.pl/chaos/ eng/”
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
