A Robust Polyscale Length Complexity Measure for Stochastic Self-Affine Processes

Abstract

Cognitive and other nonlinear systems often involve deterministic differentiable processes and stochastic non-differentiable processes. Measuring the complexity of such processes is important when extracting objective features from the processes for their classification in either reactive, or adaptive, or predictive control. This applies to classifiers based not only to the traditional neural networks, but also to deep learning systems, and particularly in cognitive systems. This paper describes a robust algorithm to measure the length complexity of a self-affine time series using multiscale and polyscale analyses, and provides new insight in the theoretical and practical aspects of extracting the measure.