Source-linked AI summary
Cross-Recurrence Quantification Analysis of Categorical and Continuous Time Series: an R package
Moreno I. Coco, Rick Dale
TL;DR
The research community lacked an efficient open-source R library for cross-recurrence analysis of interacting time series. This paper explains CRQA, presents the crqa package, and reports greater computational efficiency with consistent measures compared with crptoolbox.
Problem
The research community lacked an efficient open-source R library for cross-recurrence quantification analysis.
Method
The paper explains cross-recurrence principles and presents crqa, an R package that quantifies recurrence patterns and interaction dynamics between two time series.
Results
crqa was computationally more efficient than crptoolbox as set sizes increased while returning measures consistent with the MATLAB toolbox.
Takeaways & Limitations
CRQA distinguishes co-visitation from correlation and provides a framework for characterizing dynamic relationships between interacting time series.
Takeaways & Limitations
crqa does not yet substitute for crptoolbox because it lacks its graphical interface, plotting functionality, and additional recurrence measures.
Abstract
from arXiv · showhide
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.
Motivating Recurrence: Aggregation, Covariance, and Co-Visitation
The section distinguishes aggregation, cross-correlation, and cross-recurrence by showing that CRQA quantifies temporal co-visitation and coupling rather than only raw occurrence rates or aggregate co-variation. It motivates CRQA for categorical and continuous interaction data, including alignment delays and changes in recurrence over time.
- Conceptual distinctions: CRQA quantifies co-visitation patterns in recurrence plots and can produce information similar to cross-correlation under a different interpretive scheme.Recurrence density can vary across experimental conditions, and CRQA offers a range of extractable measures.
- Conceptual distinctions: Unlike cross-correlation, cross-recurrence can remove nonevent matches, which cross-correlation preserves and implicitly counts toward co-variation.This distinction means recurrence measures can behave differently depending on event occurrence rates.
- Conceptual distinctions: Aggregation summarizes raw event occurrence, whereas cross-correlation and cross-recurrence reveal temporal relationships between systems.Cross-correlation measures aggregate co-variation; cross-recurrence measures co-visitation and can provide more detailed temporal information.
- Interactional applications: CRQA can quantify listener alignment delays, overall alignment, and information-feedback dynamics as actions are incrementally exchanged in dialogue.For categorical data, recurrence can be computed across all state pairings and lags using a contingency table.
- Package capabilities: The package supports diagonal-wise and windowed recurrence profiles, including maximum recurrence and its delay, as well as changes in coupling across an interaction.Its methods apply to categorical data and to continuous measures using distances and a recurrence radius.
R code 1: drpdfromts
The crqa package provides R functions for extracting cross-recurrence profiles, analyzing recurrence plots, optimizing parameters, and applying categorical contingency-table methods to time series. These functions support profile and sliding-window analyses across categorical and continuous data, returning recurrence, lag, and plot-structure measures.
- drpfromts: drpfromts extracts a cross-recurrence diagonal profile across positive and negative delays for categorical or continuous time series.It uses ws to set the delay range and radius to determine whether points are recurrent, returning a profile, maximal recurrence, and its lag.
- windowdrp: windowdrp tracks cross-recurrence through time by sliding overlapping windows and reports the time-course profile, maximal recurrence, and its time point.The analysis specifies the step, window size, lag width, data type, and recurrence radius.
- crqa: crqa examines time-delayed, embedded recurrent structures and returns measures including recurrence, diagonal and vertical structures, line lengths, and entropy.Parameters control delay, embedding dimension, distance rescaling, normalization, recurrence radius, minimum line lengths, empty vertical lines, and direct plot-based calculation; unavailable analyses return 0 or NA.
- optimizeParam: optimizeParam iteratively searches parameter combinations to optimize recurrence, returning the optimal radius, embedding dimensions, and delay.Its parameter list includes the maximum lag for average mutual information, candidate steps for local minima, and delays to evaluate.
- runcrqa: The runcrqa wrapper supports profile or window analyses and either diagonal profiles or detailed recurrence-plot measures for categorical and continuous time series.The profile method computes recurrence across lags, while the window method tracks recurrence over time; window analyses require lagwidth and windowsize.
- Categorical analyses: CTcrqa calculates categorical recurrence profiles from contingency tables, whereas calcphi returns the phi-coefficient for a specified categorical state across all considered delays.CTcrqa is restricted to categorical time series and produces a profile whose length equals the number of delays considered.