Three perspectives on complexity: entropy, compression, subsymmetry

Publication Type:

Journal Articles


The European Physical Journal Special Topics, Volume 226, Issue 15, p.3251-3272 (2017)



There is no single universally accepted definition of ‘Complexity’. There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In this paper, we explore the following perspectives on complexity: effort-to-describe (Shannon entropy&nbsp;H, Lempel-Ziv complexity&nbsp;LZ), effort-to-compress (ETC&nbsp;complexity) and degree-of-order (Subsymmetry or&nbsp;SubSym). While Shannon entropy and&nbsp;LZ&nbsp;are very popular and widely used,&nbsp;ETC&nbsp;is relatively a new complexity measure. In this paper, we also propose a novel normalized complexity measure&nbsp;SubSym&nbsp;based on the existing idea of counting the number of subsymmetries or palindromes within a sequence. We compare the performance of these complexity measures on the following tasks: (A) characterizing complexity of short binary sequences of lengths 4 to 16, (B) distinguishing periodic and chaotic time series from 1D logistic map and 2D Hénon map, (C) analyzing the complexity of stochastic time series generated from 2-state Markov chains, and (D) distinguishing between tonic and irregular spiking patterns generated from the ‘Adaptive exponential integrate-and-fire’ neuron model. Our study reveals that each perspective has its own advantages and uniqueness while also having an overlap with each other