On circular correlation for data on the torus

Zhan, Xiaoping; Ma, Tao; Liu, Shuangzhe; Shimizu, Kunio

doi:10.1007/s00362-017-0897-5

Cited by 16 publications

(16 citation statements)

References 24 publications

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“…In a critique of circular-circular correlation, Zhan et al (2017) argued that the sine of an angle contains less information than the angle itself, as multiple angles can take the same sine value. Furthermore, since the sine function is not monotone within an interval of π , this may lead to unreasonable results.…”

Section: Methodsmentioning

confidence: 99%

“…Furthermore, since the sine function is not monotone within an interval of π , this may lead to unreasonable results. To circumvent these issues, they introduced a circular correlation coefficient for bivariate directional data on a torus, which is the equivalent to the product of two circles ( Sojakova, 2016 ; Zhan et al, 2017 ).…”

Section: Methodsmentioning

confidence: 99%

“…The use of Phase Locking Value (PLV) ( Boccaletti et al, 2018 ; Glerean et al, 2012 ; Pauen and Ivanova, 2013 ) to capture time-varying relationship between a pair of signals has recently been used in this context ( Rebollo et al, 2018 ). In this paper, we propose two other measures that can capture the time-varying relationship between a pair of signals: circular-circular correlation ( Jammalamadaka and Sengupta, 2001 ; Pauen and Ivanova, 2013 ), and toroidal-circular correlation ( Zhan et al, 2017 ). Importantly, this class of methods suffers from similar issues as sliding-window correlations, such as the need to select an a priori window length for analysis.…”

Section: Introductionmentioning

confidence: 99%

“…We continue by introducing a number of different methods for evaluating phase synchronization. We focus both on methods already in common use, such as the phase locking value and phase coherence, as well as methods new to the fMRI literature, such as circular-circular correlation and toroidal-circular correlation ( Zhan et al, 2017 ). Finally, we propose a new variant of phase coherence, denoted the Cosine of the Relative Phase (CRP), that can be used to compute IPS.…”

Section: Introductionmentioning

confidence: 99%

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Evaluating phase synchronization methods in fMRI: A comparison study and new approaches

2021

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In recent years there has been growing interest in measuring time-varying functional connectivity between different brain regions using resting-state functional magnetic resonance imaging (rs-fMRI) data. One way to assess the relationship between signals from different brain regions is to measure their phase synchronization (PS) across time. There are several ways to perform such analyses, and we compare methods that utilize a PS metric together with a sliding window, referred to here as windowed phase synchronization (WPS), with those that directly measure the instantaneous phase synchronization (IPS). In particular, IPS has recently gained popularity as it offers single time-point resolution of time-resolved fMRI connectivity. In this paper, we discuss the underlying assumptions required for performing PS analyses and emphasize the importance of band-pass filtering the data to obtain valid results. Further, we contrast this approach with the use of Empirical Mode Decomposition (EMD) to achieve similar goals. We review various methods for evaluating PS and introduce a new approach within the IPS framework denoted the cosine of the relative phase (CRP). We contrast methods through a series of simulations and application to rs-fMRI data. Our results indicate that CRP outperforms other tested methods and overcomes issues related to undetected temporal transitions from positive to negative associations common in IPS analysis. Further, in contrast to phase coherence, CRP unfolds the distribution of PS measures, which benefits subsequent clustering of PS matrices into recurring brain states.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Evaluating phase synchronization methods in fMRI: A comparison study and new approaches

2021

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“…Notadamente que observações sobre a direção dos ventos com base no uso do método de estatística circular tem como alicerce os pontos cardeais da rosa-dos-ventos (Zhan et al,2019). Desta forma os ciclos temporalizados de maneira mensurados diariamente, mensalmente, anualmente ou por hora, remontam a base de dados para uso com o método.…”

Section: Estatística Circularunclassified

Modelagem da direção do vento em Patos na Paraíba utilizando a distribuição de probabilidade de von Mises

Santos

Pereira

Silva

et al. 2020

RSD

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Objetivo: utilizamos a distribuição de probabilidade circular de von Mises para determinar a direção predominante do vento em Patos na Paraíba. Método: utilizaram-se dados horários de direção do vento circular, obtidos pelo Instituto Nacional de Meteorologia – INMET, no período de 21 de julho de 2007 a 30 de setembro de 2018. Foi aplicada estatística circular aos dados, mais precisamente, a distribuição de von Mises. Resultados: Os resultados das análises demonstraram que a distribuição de von Mises se ajustou bem aos dados de direção de vento, verificando que a direção do vento nesse município está com uma alta variação no sentido Sudeste. Conclusão: A análise permitiu ser uma ferramenta útil para uma possível instalação de um parque eólico, obtendo um maior aproveitamento da direção do vento, na localidade.

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