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Title: A scale-dependent measure of system dimensionality
A fundamental problem in science is uncovering the effective number of degrees of freedom in a complex system: its dimensionality. A system’s dimensionality depends on its spatiotemporal scale. Here, we introduce a scale-dependent generalization of a classic enumeration of latent variables, the participation ratio. We demonstrate how the scale-dependent participation ratio identifies the appropriate dimension at local, intermediate, and global scales in several systems such as the Lorenz attractor, hidden Markov models, and switching linear dynamical systems. We show analytically how, at different limiting scales, the scale-dependent participation ratio relates to well-established measures of dimensionality. This measure applied in neural population recordings across multiple brain areas and brain states shows fundamental trends in the dimensionality of neural activity—for example, in behaviorally engaged versus spontaneous states. Our novel method unifies widely used measures of dimensionality and applies broadly to multivariate data across several fields of science.  more » « less
Award ID(s):
2024364 2019976
PAR ID:
10355077
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
Patterns
Volume:
3
Issue:
8
ISSN:
2666-3899
Page Range / eLocation ID:
100555
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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