Discriminating disorders and their complexity

Knowledge of the dynamics nature is essential for efficient system modeling, whereas the assessment of its complexity is useful for quantifying predictability. Depending on the nature of the information source, complexity can be ordered or disordered, although most existing methods do not specify this nature. In this paper, we present a novel determinism index as an efficient measure to determine the nature of data through the complexity of the ordinal pattern slope sum (sCOPSS). Combining the above index with the sCOPSS yields a comprehensive tool for estimating the complexity and disorder of short observations. Our results provide a negative complexity for deterministic data and a positive complexity for stochastic data and mixtures of stochastic and deterministic data, thus allowing identification among them. Mixing chaotic and stochastic data reveals a resonance phenomenon in sCOPSS that allows further reduction of the requirement for data length and improves the separability of the method. Applications to real-world data are given for the identification of audio signals and the classification of electrocardiogram beats. The results obtained confirm the effectiveness of the signed complexity for discriminating disorders and their complexity from short time series, thus separating sources in mixed data.