RT Journal Article
T1 Correlation dimension of high-dimensional and high-definition experimental time series
A1 Makarov Slizneva, Valeriy
A1 Muñoz, Ricardo
A1 Herreras, Oscar
A1 Makarova, Julia
AB 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.
PB AIP Publishing
YR 2023
FD 2023
LK https://hdl.handle.net/20.500.14352/130234
UL https://hdl.handle.net/20.500.14352/130234
LA eng
DS Docta Complutense
RD 8 abr 2026