Discovering multiscale and self-similar structure with data-driven wavelets.

ABSTRACT: Many materials, processes, and structures in science and engineering have important features at multiple scales of time and/or space; examples include biological tissues, active matter, oceans, networks, and images. Explicitly extracting, describing, and defining such features are difficult tasks, at least in part because each system has a unique set of features. Here, we introduce an analysis method that, given a set of observations, discovers an energetic hierarchy of structures localized in scale and space. We call the resulting basis vectors a "data-driven wavelet decomposition." We show that this decomposition reflects the inherent structure of the dataset it acts on, whether it has no structure, structure dominated by a single scale, or structure on a hierarchy of scales. In particul

SUBMITTER: Floryan D 

PROVIDER: S-EPMC7817118 | biostudies-literature | 2021 Jan

REPOSITORIES: biostudies-literature