Comparison of Cross-Correlation and Joint-Recurrence Quantification Analysis Based Methods for Estimating Coupling Strength in Non-linear Systems
| Autor: | Kevin Shockley, Gregory J. Funke, Michael T. Tolston |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Multivariate statistics Cross-correlation Computer science Applied Mathematics lcsh:T57-57.97 Complex system physiological networks complex network analysis 01 natural sciences Stability (probability) interpersonal coordination 010305 fluids & plasmas Nonlinear system Recurrence quantification analysis 0103 physical sciences lcsh:Applied mathematics. Quantitative methods Truncation (statistics) Time series lcsh:Probabilities. Mathematical statistics 010306 general physics recurrence quantification analysis (RQA) joint recurrence quantification analysis lcsh:QA273-280 Algorithm |
| Zdroj: | Frontiers in Applied Mathematics and Statistics, Vol 6 (2020) |
| ISSN: | 2297-4687 |
| DOI: | 10.3389/fams.2020.00001/full |
| Popis: | Time-delay stability (TDS) analysis is a method for quantifying interactions in multivariate systems by identifying stable temporal relationships in time series data [1]. This method has been used to create network representations of complex systems. As originally presented, the TDS method relies on cross-correlation—a linear analysis that is restricted to estimating relationships between unidimensional time series, and which, by itself, often does not adequately characterize interactions between many non-linear complex systems of theoretical and practical interest. Thus, modifying TDS so that it relies on joint recurrence quantification analysis (JRQA), an intrinsically non-linear multidimensional framework, and then comparing the ability of the two approaches to detect interactions in non-linear systems is an important task. In the present work, we first show how TDS can be extended using JRQA, a method which is capable of multidimensional assessment of relationships in non-linear systems. In our application of JRQA, we introduce a modification in the form of a weighting factor that accounts for the truncation of time series that results from time-delayed JRQA. We also modify TDS by correcting for a bias in the method and show how analogs of recurrence-based metrics can also be obtained for TDS. We evaluate how TDS results obtained with JRQA compare to those obtained with cross-correlation for known dynamics of coupled non-linear oscillators and from unknown dynamics of multivariate behavioral signals measured from dyads performing a joint problem-solving task. We conclude that TDS using cross-correlation provides results that are comparable to those obtained with JRQA at a much-reduced computational cost. |
| Databáze: | OpenAIRE |
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