Fig 2 - uploaded by 𝙽𝚘𝚛𝚋𝚎𝚛𝚝 𝙼𝚊𝚛𝚠𝚊𝚗
Content may be subject to copyright.
Source publication
In the last two decades recurrence plots (RPs)were introduced in many different
scientific disciplines. It turned out how powerful this method is. After introducing approaches of quantification of RPs and
by
the study of relationships between RPs and fundamental properties of dynamical systems, this method attracted even more attention.
After 20 y...
Contexts in source publication
Context 1
... first years were characterised by a rather rare application of this method (Fig. 2). The appearance of recurrence plots in publications was somehow exotic. Moreover, up to this time, recurrence plots were just a visualisation tool, what yielded to the disadvantage that the user had to detect and interpret the patterns and structures revealed by the recurrence plot. Low screen and printer resolutions further worsened ...
Context 2
... major methodological work on the RP and RQA during the 1990s was performed by the group around Zbilut and Webber in Chicago. Since the mid-1990s, the scientific com- munity became more and more aware of RPs, as the continuously increasing number of publications between 1996 and 2004 demonstrates (Fig. ...
Context 3
... the last years, RPs again received more attention. Since 2005, more than 50 publications appear per year (Fig. 2). Whereas in the beginning of the applications of RPs, the method was mainly applied in life sciences (e.g. cardiology, neuro-psychology), the method became popular in other scientific fields during the years. Starting in 1994, a first application in earth sciences [25], in 1996 in finance [12], and in 1999 in engineering [7], chemistry ...
Similar publications
The clustering of time series from oscillating dynamical systems requires appropriately selected features. We employed features stemming from methods of linear and nonlinear analysis of time series, such as autocorrelation and Lyapunov exponents, as well as features estimating oscillation characteristics. Optimal feature forward selection and stand...
In this article we use time series analysis methods such as recurrence
quantification analysis, estimation of the correlation dimension
and Liapunov exponents to study three different musical compositions.
The results suggest a different level of complexity and chaoticity with
respect to the degree of freedom of the composition style.
Citations
... Our analysis ini-tiates with phase space reconstruction, embedding time series data into a higher-dimensional space to unveil hidden dynamics previously obscured in the original signal. Subsequently, we employ recurrence analysis, utilizing techniques like Recurrence Plots (RPs) to analyze relationships between points within the reconstructed phase space, extracting essential recurrence metrics that quantitatively characterize the system's behavior 22 . ...
... Following noise filtering, we conducted various Recurrence Quantitative Analysis (RQA) measures 22 , including determinism, laminarity, mean recurrence time, and recurrence time entropy, with the results depicted in Fig. 9. In Fig. 9(a), determinism values for the discussed cases are compared, revealing higher determinism in the healthy bearing compared to the faulty and rubbing bearings, with the fault bearing exhibiting less determinism than the rubbing bearing. ...
The study investigates the vibration dynamics and failure prediction of ball bearings under common failure scenarios. The experiments involve normal bearings, faulty bearings, and conditions involving external rubbing. Various analyses such as time series analysis, Fast Fourier Transform, recurrence analysis, and the Dragon-King test are employed for the classification of different vibrations created in the system. These analyses aim to assess the condition of faulty bearings and detect any anomalies or extreme events. The complementary cumulative distribution function (CCDF) proves to be an effective method for identifying outliers in temporal data, providing the probability of events in the time series. The CCDF plot is specifically utilized to reveal the probability of a dragon-king extreme event in the case of rubbing. Extracting essential recurrence metrics from Recurrence Plots, such as recurrence rate, mean recurrence time, recurrence time entropy, laminarity, and determinism, allows for a quantitative understanding of the system's behavior. The study contributes valuable insights into the vibrational characteristics of ball bearings and offers a robust methodology for predicting failures and identifying abnormal events in complex mechanical systems.
... i.e., the maximum distance along any k th dimension is chosen as the distance between the two vectors. A historical review and the application of recurrence based methods is seen in 60,61 . ...
Speech is produced by a nonlinear, dynamical Vocal Tract (VT) system, and is transmitted through multiple (air, bone and skin conduction) modes, as captured by the air, bone and throat microphones respectively. Speaker specific characteristics that capture this nonlinearity are rarely used as stand-alone features for speaker modeling, and at best have been used in tandem with well known linear spectral features to produce tangible results. This paper proposes Recurrent Plot (RP) embeddings as stand-alone, non-linear speaker-discriminating features. Two datasets, the continuous multimodal TIMIT speech corpus and the consonant-vowel unimodal syllable dataset, are used in this study for conducting closed-set speaker identification experiments. Experiments with unimodal speaker recognition systems show that RP embeddings capture the nonlinear dynamics of the VT system which are unique to every speaker, in all the modes of speech. The Air (A), Bone (B) and Throat (T) microphone systems, trained purely on RP embeddings perform with an accuracy of 95.81%, 98.18% and 99.74%, respectively. Experiments using the joint feature space of combined RP embeddings for bimodal (A–T, A–B, B–T) and trimodal (A–B–T) systems show that the best trimodal system (99.84% accuracy) performs on par with trimodal systems using spectrogram (99.45%) and MFCC (99.98%). The 98.84% performance of the B–T bimodal system shows the efficacy of a speaker recognition system based entirely on alternate (bone and throat) speech, in the absence of the standard (air) speech. The results underscore the significance of the RP embedding, as a nonlinear feature representation of the dynamical VT system that can act independently for speaker recognition. It is envisaged that speech recognition too will benefit from this nonlinear feature.
... Цей метод аналізу дозволяє систематично враховувати попередні дані та прогнозувати майбутні тенденції в енергетичній сфері. Використання рекурентного аналізу дозволяє підтримувати стабільність в енергетичних системах шляхом адаптації до змін у виробництві, споживанні та інших факторах [4][5]. Крім того, цей підхід дозволяє виявляти потенційні проблеми та ризики заздалегідь, що допомагає уникнути аварійних ситуацій та забезпечує безперебійну роботу енергетичних систем. ...
Інтеграція рекурентного аналізу у процеси в енергетиці відкриває нові можливості для оптимізації та ефективності виробництва енергії. Цей метод аналізу дозволяє систематично враховувати попередні дані та прогнозувати майбутні тенденції в енергетичній сфері. Використання рекурентного аналізу дозволяє підтримувати стабільність в енергетичних системах шляхом адаптації до змін у виробництві, споживанні та інших факторах [4-5]. Крім того, цей підхід дозволяє виявляти потенційні проблеми та ризики заздалегідь, що допомагає уникнути аварійних ситуацій та забезпечує безперебійну роботу енергетичних систем. В результаті інтеграції рекурентного аналізу, енергетичні компанії можуть оптимізувати свої процеси, зменшити витрати та підвищити загальну ефективність своєї діяльності.
... Uma dessas metodologias é o uso combinado dos Gráficos de Recorrência (Recurrence Plots, RPs) e da Análise Quantitativa de Recorrência (Recurrence Quantification Analysis -RQA). Os RPs servem como um método visual para investigar a recorrência de estados em sistemas dinâmicos através de séries temporais, enquanto a RQA aprofunda a análise ao quantificar as estruturas e a complexidade desses padrões (Selskii et al., 2023;Kecik et al., 2017;Marwan, 2008;Marwan et al., 2007). O desenvolvimento dos RPs está atrelado a questões conceituais introduzidas no trabalho de Henri Poincaré acerca do problema de três corpos (Poincaré & Sémirot, 1952). ...
Ao analisar dados recorrentes de séries temporais micrometeorológicas, os pesquisadores podem detectar padrões semelhantes e compreender os regimes turbulentos frente as suas classificações. Nessa pesquisa foi aplicado o método não-linear dos RPs (Recurrence Plot) e RQA (Recurrence Quantification Analysis) aos regimes turbulentos classificados segundo a teoria HOST, para as variáveis de velocidade e temperatura virtual, respectivamente, V e T_v de dados coletados durante o Projeto GoAmazon 2014/15. A não-estacionariedade das séries temporais analisadas foram capturadas pelos RPs, que mostraram uma variabilidade ao redor da linha de instabilidade (LOI). Os resultados sugerem uma maior estabilidade para as séries temporais de V quando comparada a variável T_v. O regime turbulento 1, caracterizado por menores valores de V e maiores para T_v, apresentaram maior complexidade nos seus RPs, e assim, maiores valores para a entropia, o que está em acordo com a teoria para turbulência, visto que a supressão da mistura vertical e a dissipação da turbulência, resulta em padrões de fluxo mais complexos próximos à superfície.
... The concept of recurrence in dynamical systems, prominent for example in recurrence quantification analysis, has developed into a well-studied field of research [52]. As an extensive amount of literature on this topic is already available, for example in [51,53], only a short introduction will be given in this section. Following the notation in [21], a recurrence plot is computed as follows. ...
... However, since RP is typically used to analyze the recurrence patterns of a single time series, further extensions are required to analyze the similar patterns between pairwise time series. Marwan et al proposed the concept of cross-RPs (CRP) [13], which simultaneously embeds two time series into phase space and compares their dynamic behaviors [20]. The cross-RP (CRP) displays all times when the state of a dynamic system occurs simultaneously in the second dynamic system, providing a two-dimensional cross-recurrence matrix. ...
... Similarly, quantification tools based on CRP, such as cross-RQA (CRQA), can measure how and to what extent two time series exhibit similar patterns. This analysis framework was initially developed and widely used in natural sciences, such as heart rate variability, seismology, and chemical fluctuations, among other fields [13,20]. In psychology, it has found extensive applications in the field of motor control [21][22][23]. ...
... Conversely, if it is too large, each state will occur with lower frequency, resulting in very few edges in the CRN and making it challenging to extract useful information. Considering the application of recurrence-based methods on shorter time series, an empirical range for n could be between [10,20]. Consider a two-dimensional time series {X t , Y t ; t ⩾ 0}, where the components have the same state space (a 1 , a 2 , . . . ...
Exploring the synchronicity between time series, especially the similar patterns during extreme events, has been a focal point of research in academia. This is due to the fact that such special dependence occurring between pairs of time series often plays a crucial role in triggering emergent behaviors in the underlying systems and is closely related to systemic risks. In this paper, we investigate the relationship between the synchronicity of time series and the corresponding topological properties of the cross-recurrence network. We discover a positive linear relationship between the probability of pairwise time series event synchronicity and the corresponding cross-recurrence network's clustering coefficient. We first provide theoretical proof, then demonstrate this relationship through simulation experiments by coupled map lattices. Finally, we empirically analyze three instances from financial systems, Earth's ecological systems, and human interactive behavioral systems to validate that this regularity is a homomorphic law in different complex systems. The discovered regularity holds significant potential for applications in monitoring financial system risks, extreme weather events, and more.
... However, we did not observe single train or cumulative train effects on the early local TEP quantified using standard methods. In contrast, exploratory analyses revealed that single TMS trains may induce non-local effects on the evoked response as well as early local effects when using more sophisticated methods [28][29][30] . Together, this work provides foundational knowledge relevant for the monitoring of transient neural changes during rTMS that can be used to guide the next generation of treatments. ...
... To evaluate whether TMS trains aligned the phase of neural oscillations (phase synchronization), we used recurrence quantification analysis (RQA). This is a dynamical systems approach to understanding complex dynamics that arise from phase shifting of oscillatory signals (see 30 for a review) and specifically for identifying transitions between coordinated and uncoordinated dynamics in a complex system 60 . In RQA, a time series is compared to itself with a predefined lag time to isolate phase regularity. ...
... EEG complexity due to oscillatory phase shifting was quantified using RQA [28][29][30] . This analysis on percent determinism revealed significant main effects of stimulation (F(1,15) = 5.2452, p = 0.0369), no main effects of probe latency (F(1,15) = 0.3869, p = 0.5433), and no stimulation by probe latency interactions (F(1,15) = 0.4596, p = 0.5082). ...
How does a train of TMS pulses modify neural activity in humans? Despite adoption of repetitive TMS (rTMS) for the treatment of neuropsychiatric disorders, we still do not understand how rTMS changes the human brain. This limited understanding stems in part from a lack of methods for noninvasively measuring the neural effects of a single TMS train—a fundamental building block of treatment—as well as the cumulative effects of consecutive TMS trains. Gaining this understanding would provide foundational knowledge to guide the next generation of treatments. Here, to overcome this limitation, we developed methods to noninvasively measure causal and acute changes in cortical excitability and evaluated this neural response to single and sequential TMS trains. In 16 healthy adults, standard 10 Hz trains were applied to the dorsolateral prefrontal cortex in a randomized, sham-controlled, event-related design and changes were assessed based on the TMS-evoked potential (TEP), a measure of cortical excitability. We hypothesized that single TMS trains would induce changes in the local TEP amplitude and that those changes would accumulate across sequential trains, but primary analyses did not indicate evidence in support of either of these hypotheses. Exploratory analyses demonstrated non-local neural changes in sensor and source space and local neural changes in phase and source space. Together these results suggest that single and sequential TMS trains may not be sufficient to modulate local cortical excitability indexed by typical TEP amplitude metrics but may cause neural changes that can be detected outside the stimulation area or using phase or source space metrics. This work should be contextualized as methods development for the monitoring of transient noninvasive neural changes during rTMS and contributes to a growing understanding of the neural effects of rTMS.
... Distance and recurrence plots [11,12]: Recurrence plots are graphical representations of the recurrence of a signal's pattern. They are created by comparing each point in a signal to all other points and determining if they are close enough to be considered recurrent. ...
A novel approach to anomaly detection in time series data is based on the use of multivariate image analysis techniques. With this approach, time series are encoded as images that make them amenable to analysis by pretrained deep neural networks. Few studies have evaluated the merits of the different image encoding algorithms, and in this investigation, encoding of time series data with Euclidean distance plots or unthresholded recurrence plots, Gramian angular fields, Morlet wavelet scalograms, and an ad hoc approach based on the presentation of the raw time series data in a stacked format are compared. This is done based on three case studies where features are extracted from the images with gray level co-occurrence matrices, local binary patterns and the use of a pretrained convolutional neural network, GoogleNet. Although no method consistently outperformed all the other methods, the Euclidean distance plots and GoogleNet features yielded the best results.
... And using GPUs acceleration the model can be trained and optimized quickly. Secondly, RP plots can preserve all the features of a time series as it is converted to an image [33,34], this implies more and more direct characterization relationships for time series. ...
Underground gas sensors as the most intuitive tool for monitoring gas concentrations in underground mining, yet they are subject to frequent anomalies due to ground pressure, constructions, even malicious masking by workers. Due to the depth of underground mining and the complexity of the environment, it is almost impossible to manually monitor the status of the all the sensors. Thus, the ability to accurately identify the working status of gas sensors at the working face are critical importance to mining safety. In this paper, we propose a deep learning feature engineering based approach to coupling the relationship between underground sensors. Experiment results show that the relationship between gas sensors can be expressed by position and time, so that when a sensor such as upper corner T0 malfunctions, it can be detected by other sensors such as T1 and T2. By converting the gas concentration into the form of recurrence plots (RPs), we are able to transform time-series gas concentration data into images with more dimensions in time lag, and enabling the application of more efficient and accurate machine vision methods. Based on the location of sensors at the working face, we found that the sensors at positions T0, T1 and T2 are correlated as the wind flows through the tunnel and have a higher correlation in the subsections of the time series. And those correlation can directly use to check the operating status of the sensors. We also discuss whether the relationships between the data itself can be preserved at the feature level during the mapping of gas concentrations to features, since deep learning (DL) looks like the next promise future after digitization in the mining industrialization with more and more data analysis and placing the results under a larger decision. This feature-based approach for gas concentration analysis can also be used for prediction and early warning.
... Different indicators, devised to investigate the dynamics of complex systems, can be derived from recurrence analysis (80). Recurrent behavior, ranging from periodicities to irregular cyclicities, is a distinct aspect of most natural processes. ...
... One of the most effective tools to investigate recurrent behaviors are the so-called recurrence plots (RPs) (80). An RP is the plot of a matrix, which describes how phase space trajectories visit the same regions in phase space. ...
... where Θ is the Heaviside function, N is the number of samples, "m" the dimension of the embedded phase space, || ||° is a norm, is a suitably chosen threshold and the i and j subscripts indicate two time points (80). When the distance of phase space values at times i and j is smaller than the threshold, the Heaviside function assumes the value of one; otherwise it is zero. ...
The coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), broke out in December 2019 in Wuhan city, in the Hubei province of China. Since then, it has spread practically all over the world, disrupting many human activities. In temperate climates overwhelming evidence indicates that its incidence increases significantly during the cold season. Italy was one of the first nations, in which COVID-19 reached epidemic proportions, already at the beginning of 2020. There is therefore enough data to perform a systematic investigation of the correlation between the spread of the virus and the environmental conditions. The objective of this study is the investigation of the relationship between the virus diffusion and the weather, including temperature, wind, humidity and air quality, before the rollout of any vaccine and including rapid variation of the pollutants (not only their long term effects as reported in the literature). Regarding them methodology, given the complexity of the problem and the sparse data, robust statistical tools based on ranking (Spearman and Kendall correlation coefficients) and innovative dynamical system analysis techniques (recurrence plots) have been deployed to disentangle the different influences. In terms of results, the evidence indicates that, even if temperature plays a fundamental role, the morbidity of COVID-19 depends also on other factors. At the aggregate level of major cities, air pollution and the environmental quantities affecting it, particularly the wind intensity, have no negligible effect. This evidence should motivate a rethinking of the public policies related to the containment of this type of airborne infectious diseases, particularly information gathering and traffic management.
