Department of Psychology.
Psychol Methods. 2022 Feb;27(1):82-98. doi: 10.1037/met0000386. Epub 2021 Jan 28.
Temporal complexity refers to qualities of a time series that are emergent, erratic, or not easily described by linear processes. Quantifying temporal complexity within a system is key to understanding the time based dynamics of said system. However, many current methods of complexity quantification are not widely used in psychological research because of their technical difficulty, computational intensity, or large number of required data samples. These requirements impede the study of complexity in many areas of psychological science. A method is presented, which overcomes these difficulties and allows for complexity quantification in relatively short time series, such as those typically obtained from psychological studies. Tangle is a measure of how dissimilar a given process is from simple periodic motion. Tangle relies on the use of a three-dimensional time delay embedding of a one-dimensional time series. This embedding is then iteratively scaled and premultiplied by a modified upshift matrix until a convergence criterion is reached. The efficacy of tangle is shown on five mathematical time series and using emotional stability, anxiety time series data obtained from 65 socially anxious participants over a 5-week period, and positive affect time series derived from a single participant who experienced a major depression episode during measurement. Simulation results show tangle is able to distinguish between different complex temporal systems in time series with as few as 50 samples. Tangle shows promise as a reliable quantification of irregular behavior of a time series. Unlike many other complexity quantification metrics, tangle is technically simple to implement and is able to uncover meaningful information about time series derived from psychological research studies. (PsycInfo Database Record (c) 2022 APA, all rights reserved).
时间复杂性是指时间序列中具有突现性、不规则性或不易用线性过程描述的性质。量化系统中的时间复杂性是理解系统基于时间的动态的关键。然而，由于技术难度、计算强度或所需数据样本数量多，许多当前的复杂性量化方法在心理学研究中并未得到广泛应用。这些要求阻碍了心理学科学许多领域对复杂性的研究。本文提出了一种方法，该方法克服了这些困难，并允许在相对较短的时间序列中进行复杂性量化，例如那些通常从心理学研究中获得的时间序列。缠结是衡量给定过程与简单周期性运动的差异程度的一种度量。缠结依赖于对一维时间序列的三维时间延迟嵌入的使用。然后，将该嵌入进行迭代缩放，并与修改后的移位矩阵相乘，直到达到收敛标准。缠结的有效性在五个数学时间序列上得到了证明，并使用了 65 名社交焦虑参与者在 5 周内的焦虑时间序列数据和来自一位在测量期间经历重度抑郁症发作的单一参与者的积极情绪时间序列。模拟结果表明，缠结能够区分时间序列中具有较少样本（低至 50 个样本）的不同复杂时间系统。缠结作为一种可靠的时间序列不规则行为量化方法具有很大的应用前景。与许多其他复杂性量化指标不同，缠结在技术上实现简单，并且能够揭示来自心理学研究的时间序列的有意义信息。（PsycInfo 数据库记录（c）2022 APA，保留所有权利）。
