Cross-Recurrence Quantification Analysis of Categorical and Continuous Time Series: an R package (1310.0201v2)

Abstract: This paper describes the R package crqa to perform cross-recurrence quantification analysis of two time series of either a categorical or continuous nature. Streams of behavioral information, from eye movements to linguistic elements, unfold over time. When two people interact, such as in conversation, they often adapt to each other, leading these behavioral levels to exhibit recurrent states. In dialogue, for example, interlocutors adapt to each other by exchanging interactive cues: smiles, nods, gestures, choice of words, and so on. In order for us to capture closely the goings-on of dynamic interaction, and uncover the extent of coupling between two individuals, we need to quantify how much recurrence is taking place at these levels. Methods available in crqa would allow researchers in cognitive science to pose such questions as how much are two people recurrent at some level of analysis, what is the characteristic lag time for one person to maximally match another, or whether one person is leading another. First, we set the theoretical ground to understand the difference between 'correlation' and 'co-visitation' when comparing two time series, using an aggregative or cross-recurrence approach. Then, we describe more formally the principles of cross-recurrence, and show with the current package how to carry out analyses applying them. We end the paper by comparing computational efficiency, and results' consistency, of crqa R package, with the benchmark MATLAB toolbox crptoolbox. We show perfect comparability between the two libraries on both levels.

• The paper introduces the CRQA R package, which quantifies temporal interactions in both categorical and continuous time series using cross-recurrence analysis.
• It details advanced methods like diagonal-wise recurrence profiles and iterative parameter optimization to capture dynamic unfolding.
• The package demonstrates superior computational efficiency compared to MATLAB tools, making sophisticated analysis more accessible to researchers.

Cross-Recurrence Quantification Analysis of Time Series: An Examination of the CRQA R Package

The described paper presents an R package, crqa, designed to perform cross-recurrence quantification analysis (CRQA) on time series data, whether categorical or continuous. This package is aimed at researchers in cognitive science, particularly those investigating dynamic interactions in human behavior, such as dialogue. CRQA provides a means to quantify the coupling between two individual time series, offering insights beyond those derived from traditional statistical methods like correlation.

Overview of Method and Application

CRQA is presented as an advancement over traditional correlational approaches, with a focus on the temporal unfolding of interactions. While traditional methods aggregate data and often ignore temporal dynamics, CRQA captures the unfolding interaction dynamics by analyzing the coupling between two interacting time series. This method has applications across numerous behavioral domains, such as eye movement, gestures, and speech patterns.

The R package is proposed as an open-access tool for researchers who might not have access to licensed software such as the MATLAB toolbox, another prevalent tool for recurrence analysis. The CRQA package in R is shown to be not only comparable in accuracy to the MATLAB crptoolbox but also more efficient in computational performance with longer time series, an important consideration for large datasets.

Key Features of the CRQA Package

The paper provides a detailed description of the features and functionalities encompassed in the CRQA R package:

• Diagonal-wise Recurrence Profile: This provides a quick method for extracting recurrence information across time delays within a time series, crucial for identifying lag patterns in dynamic interactions.
• Cross-Recurrence Measures: The package also allows for more comprehensive analysis through cross-recurrence plots, which reveal the frequency and stability of interaction points between datasets.
• Parameter Optimization: An iterative method to optimize parameters such as radius, delay, and embedding dimensions, designed to maximize the recurrence information extracted from continuous time series data.

Discussion of Results

In tests comparing the CRQA package in R with MATLAB’s crptoolbox, the R package demonstrated comparable, if not superior, computational efficiency. Consistency in output measures such as recurrence rate, determinism percentage, and diagonal line lengths was shown to be high between the two platforms. However, some minor discrepancies in outputs were noted, possibly due to differences in entropy calculation methods and vertical line measures.

Practical and Theoretical Implications

The development and availability of crqa as an open-source tool democratizes access to sophisticated cross-recurrence analysis tools. This is particularly beneficial in the context of cognitive behavioral studies where large datasets and temporal dynamics are critical. The ability to analyze and interpret the dynamic unfolding of interactions introduces new dimensions in the paper of human communication and behavior.

Future Directions

Although the current package provides a robust toolset, future expansions could include additional metrics and functionalities, potentially making the package an even more comprehensive toolbox for cognitive scientists. The open-source nature of R and its community-driven development framework also suggest that enhancements and customizations by the user community could further refine and extend the capabilities of the CRQA package.

The introduction of CRQA into the R environment provides an important step in enhancing accessibility to complex computational tools for dynamic time series analysis, opening doors for further research into human interaction and behavioral dynamics using empirical data-driven approaches.