Quantifying Self-Organization with Optimal Wavelets

TL;DR

This paper introduces a method using optimal wavelets and a wavelet-domain hidden Markov model to quantify self-organization in systems, providing a new criterion based on statistical complexity that improves denoising and can be extended to higher dimensions.

Contribution

It presents a novel framework for quantifying self-organization using optimal wavelets and hidden Markov models, with a new criterion based on statistical complexity.

Findings

Superior denoising performance demonstrated

Framework applicable to one-dimensional data of any type

Method generalizable to higher-dimensional data

Abstract

The optimal wavelet basis is used to develop quantitative, experimentally applicable criteria for self-organization. The choice of the optimal wavelet is based on the model of self-organization in the wavelet tree. The framework of the model is founded on the wavelet-domain hidden Markov model and the optimal wavelet basis criterion for self-organization which assumes inherent increase in statistical complexity, the information content necessary for maximally accurate prediction of the system's dynamics. At the same time the method, presented here for the one-dimensional data of any type, performs superior denoising and may be easily generalized to higher dimensions.