Recurrence Quantification Analysis Measures Research Articles

Interpolation and sampling effects on recurrence quantification measures.

The recurrence plot and the recurrence quantification analysis (RQA) are well-established methods for the analysis of data from complex systems. They provide important insights into the nature of the dynamics, periodicity, regime changes, and many more. These methods are used in different fields of research, such as finance, engineering, life, and earth science. To use them, the data have usually to be uniformly sampled, posing difficulties in investigations that provide non-uniformly sampled data, as typical in medical data (e.g., heart-beat based measurements), paleoclimate archives (such as sediment cores or stalagmites), or astrophysics (supernova or pulsar observations). One frequently used solution is interpolation to generate uniform time series. However, this preprocessing step can introduce bias to the RQA measures, particularly those that rely on the diagonal or vertical line structure in the recurrence plot. Using prototypical model systems, we systematically analyze differences in the RQA measure average diagonal line length for data with different sampling and interpolation. For real data, we show that the course of this measure strongly depends on the choice of the sampling rate for interpolation. Furthermore, we suggest a correction scheme, which is capable of correcting the bias introduced by the prepossessing step if the interpolation ratio is an integer.

Recurrence Quantification Analysis of Crowd Sound Dynamics.

When multiple individuals interact in a conversation or as part of a large crowd, emergent structures and dynamics arise that are behavioral properties of the interacting group rather than of any individual member of that group. Recent work using traditional signal processing techniques and machine learning has demonstrated that global acoustic data recorded from a crowd at a basketball game can be used to classify emergent crowd behavior in terms of the crowd's purported emotional state. We propose that the description of crowd behavior from such global acoustic data could benefit from nonlinear analysis methods derived from dynamical systems theory. Such methods have been used in recent research applying nonlinear methods to audio data extracted from music and group musical interactions. In this work, we used nonlinear analyses to extract features that are relevant to the behavioral interactions that underlie acoustic signals produced by a crowd attending a sporting event. We propose that recurrence dynamics measured from these audio signals via recurrence quantification analysis (RQA) reflect information about the behavioral dynamics of the crowd itself. We analyze these dynamics from acoustic signals recorded from crowds attending basketball games, and that were manually labeled according to the crowds' emotional state across six categories: angry noise, applause, cheer, distraction noise, positive chant, and negative chant. We show that RQA measures are useful to differentiate the emergent acoustic behavioral dynamics between these categories, and can provide insight into the recurrence patterns that underlie crowd interactions.

Application of nonlinear dynamics analysis to gas-solid flow system in horizontal pneumatic conveying of plastic pellets

Chaotic invariant and recurrence quantification analysis measures have characterised fully developed gas-solid flow in horizontal pneumatic conveying of plastic pellets. These measures describe the complexity in phase spaces (attractors) and recurrence plots, reconstructed from pressure and bottom arc-shaped electrostatic signals to characterise the behaviour of flow patterns. Different flow patterns were identified using high-speed video imaging of a transparent pipeline and classified at several operating conditions in a flow pattern map and state diagram. Recurrence plots were analysed for the identified flow patterns, which showed different qualitative structures. The chaotic invariant and recurrence quantification analysis measures were correlated with the state diagram, indicating that the fluctuations of pressure senor and electrostatic sensor signals can classify the flow patterns at different operating conditions. Combining the analysis measures for electrostatic signals can indicate whether the flow condition is above, near or below the minimum energy consumption operating conditions.

Recurrence Quantification Analysis as a Form of Postural Control Assessment: A Systematic Review

Human postural control is commonly assessed by center of pressure (CoP) displacement analysis. However, traditional linear parameters do not provide a complete picture of postural control, so a number of nonlinear analyses have been introduced. One of these is recurrence quantification analysis (RQA), which is used to determine the number and duration of repeated states in a dynamic system. This review aimed to show how the RQA measures look in different groups of subjects when assessing postural stability during quiet standing and how the authors interpret them. Therefore, a systematic review was conducted of papers published from 2000 to February 2023. Searched databases were PubMed, ScienceDirect, and EBSCO. Twenty-eight publications were included in this review. The RQA parameters most commonly found in papers are %DET (determinism), ENT (Shannon entropy), %REC (recurrence), and %LAM (laminarity). %LAM is the most sensitive factor in determining differences in CoP position between different age groups, as it describes motion fluidity. The vision affects the deterministic structure of CoP motions. When the sensory organization test conditions became difficult, CoP variability increased, while the %DET decreased. It was concluded that traditional and nonlinear methods provide complementary and not redundant information for assessing age- and health-related changes in standing balance.

Distinguishing between struggling and skilled readers based on their prosodic speech patterns in oral reading: An exploratory study in grades 2 and 4

The purpose of this study was to examine if prosodic patterns in oral reading derived from Recurrence Quantification Analysis (RQA) could distinguish between struggling and skilled German readers in Grades 2 (n = 67) and 4 (n = 69). Furthermore, we investigated whether models estimated with RQA measures outperformed models estimated with prosodic features derived from prosodic transcription. According to the findings, struggling second graders appear to have a slower reading rate, longer intervals between pauses, and more repetitions of recurrent amplitudes and pauses, whereas struggling fourth graders appear to have less stable pause patterns over time, more pitch repetitions, more similar amplitude patterns over time, and more repetitions of pauses. Additionally, the models with prosodic patterns outperformed models with prosodic features. These findings suggest that the RQA approach provides additional information about prosody that complements an established approach.

Intraday Seasonality and Volatility Pattern: An Explanation with Recurrence Quantification Analysis

The Recurrence Quantification Analysis (RQA), a pattern recognition-based time series analysis method, can be successfully utilized for short, nonstationary, nonlinear, and chaotic time series. These RQA measures quantify several properties of time series, including predictability, regularity, stability, randomness, and complexity. In this regard, first, we analyzed the intraday seasonality with RQA and demonstrated how RQA measures change among the intraday periods by using 160 million row matched orders of 100 shares from Borsa Istanbul Equity Market between 2019M10 and 2020M02. We selected 50 stocks from the BIST50 Index group and 50 stocks from outside of the BIST100 Index group. Since these two share groups exhibit similar intraday RQA seasonality, our results are robust. Second, we explained intraday volatility with RQA measures and found a relationship between RQA measures and intraday volatility using a regression model.

Nonlinear Dynamics of Heart Rate Variability after Acutely Induced Myocardial Ischemia by Percutaneous Transluminal Coronary Angioplasty.

Several heart rate variability (HRV) characteristics of patients with myocardial ischemia are associated with a higher mortality risk. However, the immediate effect of acute ischemia on the HRV nonlinear dynamical behavior is unknown. The objective of this work is to explore the presence of nonlinearity through surrogate data testing and describe the dynamical behavior of HRV in acutely induced ischemia by percutaneous transluminal coronary angioplasty (PTCA) with linear and recurrence quantification analysis (RQA). Short-term electrocardiographic recordings from 68 patients before and after being treated with elective PTCA were selected from a publicly available database. The presence of nonlinear behavior was confirmed by determinism and laminarity in a relevant proportion of HRV time series, in up to 29.4% during baseline conditions and 30.9% after PTCA without statistical difference between these scenarios. After PTCA, the mean value and standard deviation of HRV time series decreased, while determinism and laminarity values increased. Here, the diminishment in overall variability caused by PTCA is not accompanied by a change in nonlinearity detection. Therefore, the presence of nonlinear behavior in HRV time series is not necessarily in agreement with the change of traditional and RQA measures.

Recurrence quantification analysis of center of pressure trajectories for balance and fall-risk assessment in young and older adults.

The prevalence and impact of balance impairments and falls in older adults have motivated several studies on the characterization of human balance. This study aimed to determine the ability of recurrence quantification analysis (RQA) measures to characterize balance control during quiet standing in young and older adults and to discriminate between different fall risk groups. We analyze center pressure trajectories in the medial-lateral and anterior-posterior directions from a publicly available static posturography dataset that contains tests acquired under four vision-surface testing conditions. Participants were retrospectively classified as young adults (age<60, n=85), non-fallers (age≥60, falls=0, n=56), and fallers (age≥60, falls≥1, n=18). Mixed ANOVA and post hoc analyzes were performed to test for differences between groups. For CoP fluctuations in the anterior-posterior direction, all RQA measures showed significantly higher values for young than older adults when standing on a compliant surface, indicating less predictable and stable balance control among seniors under testing conditions where sensory information is restricted or altered. However, no significant differences between non-fallers and fallers were observed. These results support the use of RQA to characterize balance control in young and old adults, but not to discriminate between different fall risk groups.

A time-series perspective on executive functioning: The benefits of a dynamic approach to random number generation.

Executive functioning (EF) is a key topic in neuropsychology. A multitude of underlying processes and constructs have been suggested to explain EF, which are measured by at least as many different neuropsychological tests. However, these tests often refer to summary statistics to quantify the construct under study, failing to capture the dynamic nature of EF. An alternative to these summary statistics is a time-series approach that quantifies all the available temporal information. We used recurrence quantification analysis (RQA) to quantify the characteristics of any temporal pattern in random number generation data and we compared RQA to the traditional and static analysis of random number sequences. The traditional measures yield inconsistent results with increasing sequences length, both for computer-generated and human-generated sequences, whereas the RQA measures do not. The results suggest that a time-series approach does a better job at modelling what is happening on different time-scales, and, therefore, is better at explaining how EF is changing in the course of the random number generation task. We argue that it is likely that these findings also apply to other neuropsychological EF tests, and that a time-series approach is an important addition to the study of EF.

Averaged recurrence quantification analysis

Recurrence quantification analysis (RQA) is a well established method of nonlinear data analysis. In this work, we present a new strategy for an almost parameter-free RQA. The approach finally omits the choice of the threshold parameter by calculating the RQA measures for a range of thresholds (in fact recurrence rates). Specifically, we test the ability of the RQA measure determinism, to sort data with respect to their signal to noise ratios. We consider a periodic signal, simple chaotic logistic equation, and Lorenz system in the tested data set with different and even very small signal-to-noise ratios of lengths 10^2, 10^3, 10^4, and 10^5. To make the calculations possible, a new effective algorithm was developed for streamlining of the numerical operations on graphics processing unit (GPU).

Recurrence quantification and bifurcation analysis of electrical activity in resistive/memristive synapse coupled Fitzhugh–Nagumo type neurons

Temporal response of excitable individual and coupled different neuronal circuits i.e., Cell-I and Cell-II, of Fitzhugh–Nagumo type have been numerically simulated with a view to understand and characterize the complexities of involved dynamical processes. FHN neuronal circuit Cell-I and Cell-II have been shown to exhibit supercritical Hopf bifurcation, when excited by an external steady stimulus. For time varying sinusoidal excitation, the temporal action potential behavior of these neuronal circuits, when analyzed using measures of recurrence quantification analysis (RQA) and bifurcation diagram reveals period-1, period-2, multi-periodic, chaotic and reverse period doubling characteristics as observed earlier experimentally in giant squid axon and other biological cell assemblies. Phase portrait, bifurcation diagrams and recurrence plot (RPs), of (i) unidirectional and (ii) bidirectional coupled FHN Cell-I and Cell-II, through a gap junction resistor, suggest the possibility of transition to intermittent state besides the transition of respective action potential from periodic to multi-periodic to chaotic state in an ordered or disordered fashion, depending on values of system parameters that control the complexities. Further, for both the configurations (i) and (ii), synchronization of FHN neuron Cell-I with Cell-II is also shown to occur for large values of coupling parameter, ξ. The dynamical effect of electromagnetic radiation on individual FHN neuron circuits has also been investigated using a flux controlled memristor that couples the magnetic flux with the individual FHN neurons. Phase portrait, bifurcation and RQA analysis have also been used to characterize the electrical activities of excitable cell assemblies involving memristive synapse coupled FHN neuronal Cell-I and Cell-II in settings (i) and (ii) respectively.

Evaluation of Geometric Attractor Structure and Recurrence Analysis in Professional Dancers.

Background: Human motor systems contain nonlinear features. The purpose of this study was to evaluate the geometric structure of attractors and analyze recurrence in two different pirouettes (jazz and classic) performed by 15 professional dancers. Methods: The kinematics of the body’s center of mass (CoM) and knee of the supporting leg (LKNE) during the pirouette were measured using the Vicon system. A time series of selected points were resampled, normalized, and randomly reordered. Then, every second time series was flipped to be combined with other time series and make a long time series out of the repetitions of a single task. The attractors were reconstructed, and the convex hull volumes (CHV) were counted for the CoM and LKNE for each pirouette in each direction. Recurrence quantification analysis (RQA) was used to extract additional information. Results: The CHVs calculated for the LKNE were significantly lower for the jazz pirouette. All RQA measures had the highest values for LKNE along the mediolateral axis for the jazz pirouette. This result underscores the high determinism, high motion recurrence, and complexity of this maneuver. Conclusions: The findings offer new insight into the evaluation of the approximation of homogeneity in motion control. A high determinism indicates a highly stable and predictive motion trajectory.

Global temporal typing patterns in foreign language writing: exploring language proficiency through recurrence quantification analysis (RQA)

Recurrence quantification analysis (RQA) is a time-series analysis method that uses autocorrelation properties of typing data to detect regularities within the writing process. The following paper first gives a detailed introduction to RQA and its application to time series data. We then apply RQA to keystroke logging data of first and foreign language writing to illustrate how outcome measures of RQA can be understood as skill-driven constraints on keyboard typing performance. Forty native German students performed two prompted writing assignments, one in German and one in English, a standardized copy task, and a standardized English placement test. We assumed more fluent and skilled writing to reveal more structured typing time series patterns. Accordingly, we expected writing in a well-mastered first language to coincide with higher values in relevant RQA measures as compared to writing in a foreign language. Results of mixed model ANOVAs confirmed our hypothesis. We further observed that RQA measures tend to be higher, thus indicating more structured data, whenever parameters of pause, burst, and revision analyses indicate more fluent writing. Multiple regression analyses revealed that, in addition to typing skills, language proficiency significantly predicts outcomes of RQA. Thus, the present data emphasize RQA being a valuable resource for studying time series data that yields meaningful information about the effort a writer must exert during text production.

Evaluating Operator Training Performance Using Recurrence Quantification Analysis of Autocorrelation Transformed Eye Gaze Data.

This research aimed to investigate the relationship between gaze behaviour dynamics and operator performance. Individuals differ in their approach when learning a new task often resulting in performance disparity. During training some individuals learn the structure and dynamics of the task and develop a systematic approach, whereas others may achieve the same result albeit with increased perceived workload, or indeed some may fail to achieve superior performance levels. Previous research has shown that comparing gaze of experts with novices can provide unique insights into cognitive functioning of superior performers. Twenty-five individuals participated in a computer-based simulation task. The concept of coefficient of variation (CoV) of task scores was used to compute the participants' consistency of performance. Based on CoV, the cohort was split into two performance categories. The temporal patterns in participants gaze data were transformed using autocorrelation, and recurrence quantification analysis (RQA) was employed to analyse and quantify the patterns. A Mann-Whitney U analysis demonstrated significantly (p < .01) higher determinism, entropy and laminarity in the superior group compared to the moderate group. Pearson's correlation revealed a significant (p < .01) negative correlation between the consistency of task performance (CoV) and the RQA measures. The results demonstrated that eye gaze dynamics can be used as an objective measure of performance. Participants classified as superior performers consistently demonstrated a systematic gaze activity which were in line with the task structure. The methods presented here are applicable to observe and evaluate operators' strategic distribution of gaze. Specifically, for tactical monitoring and decision making in task environments where spatial locations of elements-of-interest vary continuously.

Stability Analysis of Bitcoin using Recurrence Quantification Analysis

Cryptocurrencies are new kinds of electronic currencies based on communication technologies. These currencies have attracted the attention of investors. However, cryptocurrencies are very volatile and unpredictable. For investors, it is very difficult to make investment decisions in cryptocurrency market. Therefore, revealing changes in the dynamics of cryptocurrencies are valuable for investors. Bitcoin is the most popular and representative cryptocurrency in cryptocurrency market. In this study how dynamical properties of Bitcoin changed through time is analyzed with recurrence quantification analysis (RQA). RQA is a pattern recognition-based time series analysis method that reveals dynamics of the time series by calculating some metrics called RQA measures. This method has been successfully applied to nonlinear, nonstationary, short and chaotic time series and does not assume a statistical model. RQA can reveal important properties of time series data such as determinism, laminarity, stability, randomness, regularity and complexity. By using sliding window RQA we show that in 2021 RQA measures for Bitcoin prices collapse and Bitcoin becomes more unpredictable, more random, more unstable, more irregular and less complex. Therefore, dynamics and stability of the Bitcoin prices significantly changed in 2021.

Effects of 1Hz repetitive transcranial magnetic stimulation on autism with intellectual disability: A pilot study

ObjectiveTo explore whether 1 Hz repetitive transcranial magnetic stimulation (rTMS) has positive effects on brain activity and behavior of autistic children with intellectual disability. Methods32 autistic children with intellectual disability (26 boys and 6 girls) were recruited to participate in this feasibility study. The autistic children were divided randomly and equally into an experimental group and a control group. 16 children (three girls and 13 boys; mean ± SD age: 7.8 ± 2.1 years) who received rTMS treatment twice a week were served as the experimental group, while 16 children (three girls and 13 boys; mean ± SD age: 7.2 ± 1.6 years) with sham stimulation were considered as the control group. Recurrence quantification analysis (RQA) was employed to quantify the nonlinear features of electroencephalogram (EEG) signals recorded during the resting state. Three RQA measures, including recursive rate (RR), deterministic (DET) and mean diagonal length (L) were extracted from the EEG signals to characterize the deterministic features of cortical activity. ResultsSignificant differences in RR and DET were observed between the experimental group and the control group. We also found discernible discrepancies in the Autism Behavior Checklist (ABC) score pre- and post-rTMS for the experimental group. Conclusions1 Hz repetitive transcranial magnetic stimulation (rTMS) could positively influence brain activity and behavior of autistic children with intellectual disability.

Region-Wise Brain Response Classification of ASD Children Using EEG and BiLSTM RNN.

AbstractAutism spectrum disorder (ASD) is a neurodevelopmental disorder characterized by impairment in sensory modulation. These sensory modulation deficits would ultimately lead them to difficulties in adaptive behavior and intellectual functioning. The purpose of this study was to observe changes in the nervous system with responses to auditory/visual and only audio stimuli in children with autism and typically developing (TD) through electroencephalography (EEG). In this study, 20 children with ASD and 20 children with TD were considered to investigate the difference in the neural dynamics. The neural dynamics could be understood by non-linear analysis of the EEG signal. In this research to reveal the underlying nonlinear EEG dynamics, recurrence quantification analysis (RQA) is applied. RQA measures were analyzed using various parameter changes in RQA computations. In this research, the cosine distance metric was considered due to its capability of information retrieval and the other distance metrics parameters are compared for identifying the best biomarker. Each computational combination of the RQA measure and the responding channel was analyzed and discussed. To classify ASD and TD, the resulting features from RQA were fed to the designed BiLSTM (bi-long short-term memory) network. The classification accuracy was tested channel-wise for each combination. T3 and T5 channels with neighborhood selection as FAN (fixed amount of nearest neighbors) and distance metric as cosine is considered as the best-suited combination to discriminate between ASD and TD with the classification accuracy of 91.86%, respectively.

Reliability of Recurrence Quantification Analysis Measures for Sit-to-Stand and Stand-to-Sit Activities in Healthy Older Adults Using Wearable Sensors

Standing up and sitting down are prerequisite motions in most activities of daily living scenarios. The ability to sit down in and stand up from a chair or a bed depreciates and becomes a complex task with increasing age. Hence, research on the analysis and recognition of these two activities can help in the design of algorithms for assistive devices. In this work, we propose a reliability analysis for testing the internal consistency of nonlinear recurrence features for sit-to-stand (Si2St) and stand-to-sit (St2Si) activities for motion acceleration data collected by a wearable sensing device for 14 healthy older subjects in the age range of 78 ± 4.9 years. Four recurrence features—%recurrence rate, %determinism, entropy, and average diagonal length—were calculated by using recurrence plots for both activities. A detailed relative and absolute reliability statistical analysis based on Cronbach’s correlation coefficient (α) and standard error of measurement was performed for all recurrence measures. Correlation values as high as α = 0.68 (%determinism) and α = 0.72 (entropy) in the case of Si2St and α = 0.64 (%determinism) and α = 0.69 (entropy) in the case of St2Si—with low standard error in the measurements—show the reliability of %determinism and entropy for repeated acceleration measurements for the characterization of both the St2Si and Si2St activities in the case of healthy older adults.

Bimanual Coordination in a Whole-Body Dynamic Balance Sport, Slacklining: A Comparison of Novice and Expert.

As previous studies have suggested that bimanual coordination is important for slacklining, the authors questioned whether this important skill plays a role in the performance of a fundamental task of slacklining. To address this question, the authors compared single-leg standing on the slackline between novices and experts in terms of bimanual coordination dynamics within a dynamical systems framework using relative phase and recurrence quantification analysis measures. Five novices and five experts participated in the experiment. Participants were required to perform single-leg standing on a slackline. To collect motion data while slacklining, the authors used a 3D motion capture system and obtained time series data on the wrist position of both hands. The authors compared bimanual coordination dynamics between novices and experts. Although this preliminary study was limited in its sample size, the results suggest that experts tend to show a more antiphase coordination pattern than novices do and that they can more sustainably coordinate their hands compared with novices in terms of temporal structure in diagonal-related recurrence measures (i.e.,maxline, mean line, and percentage determinism).

Influences of Embedding Parameters and Segment Sizes in Recursive Characteristics Analysis on Coefficients of Friction

The methods of recurrence plots (RPs) and recurrence quantification analysis (RQA) have been used to investigate the tribosystem. The morphology of RPs and RQA measures are strongly dependent on the embedding parameters of the recursive matrix and the segment sizes of the time-series. To improve the calculation accuracy of recursive characteristics analysis, the influences of the embedding parameters and segment sizes on the morphology of RPs and RQA measures have been studied in this letter. Three kinds of theoretical chaotic time-series and measured coefficient of friction (COF) signals during the running-in process were chosen as research objects, and the morphology of RPs and RQA measures were obtained using CRP toolbox afterward. The results indicate that no embedding was actually needed if the data sets are to be qualitatively analyzed using RPs and RQA. Additionally, the morphology of RPs and RQA measures are sensitive to the segment sizes for theoretical chaotic time-series, while the RQA measures of COF signal in the steady-state period are rather stable due to its self-similarity. Finally, according to the guidelines of the parameter settings, the dynamical evolution of measured COF signals during the running-in process have been investigated. It is indicated that recursive characteristics of COF signals could reveal the tribological behaviors’ evolution and conduct the running-in status identification. The results in this paper are significant for improving the calculation accuracy and saving computational time when using the method of recursive characteristics analysis on the tribological behaviors.