Quantifying self-organization with optimal wavelets

Abstract

An optimal wavelet basis is used to develop a quantitative, experimentally applicable criterion 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. The principle assumes increase in statistical complexity considered as the information content necessary for maximally accurate prediction of the system's dynamics. The causal states and the wavelet machine (w-machine) are defined in analogy with the -machine constructed as the unique, minimal, predictive model of the process. The method, presented here for the one-dimensional data, concurrently performs superior denoising and may be easily generalized to higher dimensions.