2026-06-02T02:35:29Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/1302342026-01-15T00:50:38Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Makarov Slizneva, Valeriy
author
Muñoz, Ricardo
author
Herreras, Oscar
author
Makarova, Julia
2026-01-14T15:39:40Z
2026-01-14T15:39:40Z
2023
10.1063/5.0168400
https://hdl.handle.net/20.500.14352/130234
https://doi.org/10.1063/5.0168400
The correlation dimension (CD) is a nonlinear measure of the complexity of invariant sets. First introduced for describing low-dimensional chaotic attractors, it has been later extended to the analysis of experimental electroencephalographic (EEG), magnetoencephalographic (MEG), and local field potential (LFP) recordings. However, its direct application to high-dimensional (dozens of signals) and high-definition (kHz sampling rate) 2HD data revealed a controversy in the results. We show that the need for an exponentially long data sample is the main difficulty in dealing with 2HD data. Then, we provide a novel method for estimating CD that enables orders of magnitude reduction of the required sample size. The approach decomposes raw data into statistically independent components and estimates the CD for each of them separately. In addition, the method allows ongoing insights into the interplay between the complexity of the contributing components, which can be related to different anatomical pathways and brain regions. The latter opens new approaches to a deeper interpretation of experimental data. Finally, we illustrate the method with synthetic data and LFPs recorded in the hippocampus of a rat.
eng
Attribution 4.0 International
Correlation dimension of high-dimensional and high-definition experimental time series
journal article
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URL
https://docta.ucm.es/bitstreams/95ad6552-3c80-4db3-b69a-cea06bf86d15/download
File
MD5
4224c6d90c8ef6f278c328b7f97b1692
6854560
application/pdf
2023_Chaos_Mak_etal-3.pdf