scholarly journals Multivariate Multiscale Dispersion Entropy of Biomedical Times Series

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 913 ◽  
Author(s):  
Hamed Azami ◽  
Alberto Fernández ◽  
Javier Escudero
Keyword(s):  
Time Series ◽  
Multivariate Time Series ◽  
Channel Noise ◽  
Original Algorithm ◽  
Times Series ◽  
Non Linear ◽  
Long Time ◽  
Spatial Domains ◽  
The Stability ◽  
Multivariate Signals

Due to the non-linearity of numerous physiological recordings, non-linear analysis of multi-channel signals has been extensively used in biomedical engineering and neuroscience. Multivariate multiscale sample entropy (MSE–mvMSE) is a popular non-linear metric to quantify the irregularity of multi-channel time series. However, mvMSE has two main drawbacks: (1) the entropy values obtained by the original algorithm of mvMSE are either undefined or unreliable for short signals (300 sample points); and (2) the computation of mvMSE for signals with a large number of channels requires the storage of a huge number of elements. To deal with these problems and improve the stability of mvMSE, we introduce multivariate multiscale dispersion entropy (MDE–mvMDE), as an extension of our recently developed MDE, to quantify the complexity of multivariate time series. We assess mvMDE, in comparison with the state-of-the-art and most widespread multivariate approaches, namely, mvMSE and multivariate multiscale fuzzy entropy (mvMFE), on multi-channel noise signals, bivariate autoregressive processes, and three biomedical datasets. The results show that mvMDE takes into account dependencies in patterns across both the time and spatial domains. The mvMDE, mvMSE, and mvMFE methods are consistent in that they lead to similar conclusions about the underlying physiological conditions. However, the proposed mvMDE discriminates various physiological states of the biomedical recordings better than mvMSE and mvMFE. In addition, for both the short and long time series, the mvMDE-based results are noticeably more stable than the mvMSE- and mvMFE-based ones. For short multivariate time series, mvMDE, unlike mvMSE, does not result in undefined values. Furthermore, mvMDE is faster than mvMFE and mvMSE and also needs to store a considerably smaller number of elements. Due to its ability to detect different kinds of dynamics of multivariate signals, mvMDE has great potential to analyse various signals.

Do Trophic Interactions Cause Population Cycles?

2002 ◽  
Author(s):  
Alan A. Berryman
Keyword(s):  
Time Series ◽  
Multivariate Time Series ◽  
Extended Period ◽  
Population Cycles ◽  
Web Architecture ◽  
Animal Populations ◽  
Spruce Stands ◽  
Long Time ◽  
Exhaustive Study

My motivation in editing this book has been to present as compelling and credible a story as possible. Although I am personally convinced of the soundness of our argument, that food web architecture plays a key role in the cyclic dynamics of many animal populations, I am not sure that others will be so convinced. In this final chapter, therefore, I exercise my prerogative as editor to have the last word, a final attempt to convince the skeptics and to answer the critics.Perhaps the most compelling case comes from the Mikael Münster-Swendsen monumental study of a needleminer infesting Danish spruce forests (chapter 2). Mikael is the only person I know of who has, almost single-handedly, and with considerable precision, measured all the variables suspected of affecting the dynamics of a particular population over an extended period of time (19 years) and in several different localities (seven isolated spruce stands). Others have longer time series from more places, but none has been so complete in terms of the number of variables measured. This exhaustive study enabled him to build a model of the complete needleminer life system, and use this model to home in on the factors responsible for the cyclical dynamics. However, the story would not have been complete without multivariate time series analysis, which led to the discovery of parasitoids as the cause of the key feedback process, density-related reduction in fecundity. The lesson from Münster-Swendsen's work is clear: If we want to understand population dynamics, we need long time series for all the variables likely to affect the dynamics of the subject population(s). In other words, we need to consistently monitor ecological systems over long periods of time and in many different locations. If there is a weakness in his study, it is the absence of the final definitive experiment. Such an experiment would be relatively easy and cheap to do (relative to those described in other chapters), because isolated spruce stands are common in Denmark and parasitoids emerge from the soil a week or two after the needleminer. Thus, parasitoids could easily be excluded by spraying the ground with an insecticide after needleminer emergence.

scholarly journals Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 385 ◽  
Author(s):  
David Cuesta-Frau ◽  
Juan Pablo Murillo-Escobar ◽  
Diana Alexandra Orrego ◽  
Edilson Delgado-Trejos
Keyword(s):  
Time Series ◽  
Classification Performance ◽  
Permutation Entropy ◽  
Series Length ◽  
Stability Point ◽  
Long Time ◽  
Model Time Series ◽  
The Stability ◽  
Forbidden Patterns ◽  
Short Time

Permutation Entropy (PE) is a time series complexity measure commonly used in a variety of contexts, with medicine being the prime example. In its general form, it requires three input parameters for its calculation: time series length N, embedded dimension m, and embedded delay τ . Inappropriate choices of these parameters may potentially lead to incorrect interpretations. However, there are no specific guidelines for an optimal selection of N, m, or τ , only general recommendations such as N > > m ! , τ = 1 , or m = 3 , … , 7 . This paper deals specifically with the study of the practical implications of N > > m ! , since long time series are often not available, or non-stationary, and other preliminary results suggest that low N values do not necessarily invalidate PE usefulness. Our study analyses the PE variation as a function of the series length N and embedded dimension m in the context of a diverse experimental set, both synthetic (random, spikes, or logistic model time series) and real–world (climatology, seismic, financial, or biomedical time series), and the classification performance achieved with varying N and m. The results seem to indicate that shorter lengths than those suggested by N > > m ! are sufficient for a stable PE calculation, and even very short time series can be robustly classified based on PE measurements before the stability point is reached. This may be due to the fact that there are forbidden patterns in chaotic time series, not all the patterns are equally informative, and differences among classes are already apparent at very short lengths.

Exploring long-term urban cycles with multivariate time-series analysis

2021 ◽  
pp. 239980832110581
Author(s):  
Luca Salvati
Keyword(s):  
Time Series ◽  
Life Cycle ◽  
Time Series Analysis ◽  
Population Growth ◽  
Multivariate Time Series ◽  
Metropolitan Region ◽  
Series Analysis ◽  
Multivariate Time Series Analysis ◽  
Non Linear

European cities underwent long-term socioeconomic transformations resulting in a shift from centralized demographic growth typical of late industrialization to a more recent (and spatially uncoordinated) de-concentration of population and economic activities. While abandoning traditional compact models and moving toward settlement dispersion, population growth in urban areas was assumed to follow a “life cycle” constituted of four developmental stages (urbanization, suburbanization, counter-urbanization, and re-urbanization). We studied anomalies in the City Life Cycle (CLC) of a large metropolitan region (Athens, Greece) with the aim at achieving a less mechanistic interpretation of long-term population growth in complex social contexts. Using population data that cover more than 170 years (1848–2020) and multivariate time-series analysis, a non-linear growth history was delineated, with sequential accelerations and decelerations characteristic of the first CLC stage (urbanization). Considering the classical division in three radio-centric districts (core, ring, and agglomeration), different development stages coexisted since World War II. Heterogeneous suburbanization processes mixed up with late urbanization and weaker impulses of counter-urbanization and re-urbanization. The empirical results of time-series analysis confirm the non-linear expansion of Athens, shedding further light on long-term mechanisms of metropolitan development and informing management policies of urban growth.

scholarly journals A non-linear Granger-causality framework to investigate climate–vegetation dynamics

2017 ◽  
Vol 10 (5) ◽  
pp. 1945-1960 ◽  
Author(s):  
Christina Papagiannopoulou ◽  
Diego G. Miralles ◽  
Stijn Decubber ◽  
Matthias Demuzere ◽  
Niko E. C. Verhoest ◽  
...  
Keyword(s):  
Time Series ◽  
Granger Causality ◽  
Vegetation Dynamics ◽  
Global Climate ◽  
Multivariate Time Series ◽  
Predictive Modelling ◽  
Experimental Results ◽  
Causality Analysis ◽  
Climate Data ◽  
Non Linear

Abstract. Satellite Earth observation has led to the creation of global climate data records of many important environmental and climatic variables. These come in the form of multivariate time series with different spatial and temporal resolutions. Data of this kind provide new means to further unravel the influence of climate on vegetation dynamics. However, as advocated in this article, commonly used statistical methods are often too simplistic to represent complex climate–vegetation relationships due to linearity assumptions. Therefore, as an extension of linear Granger-causality analysis, we present a novel non-linear framework consisting of several components, such as data collection from various databases, time series decomposition techniques, feature construction methods, and predictive modelling by means of random forests. Experimental results on global data sets indicate that, with this framework, it is possible to detect non-linear patterns that are much less visible with traditional Granger-causality methods. In addition, we discuss extensive experimental results that highlight the importance of considering non-linear aspects of climate–vegetation dynamics.

scholarly journals Evaluation of Directed Causality Measures and Lag Estimations in Multivariate Time-Series

2021 ◽  
Vol 15 ◽  
Author(s):  
Jolan Heyse ◽  
Laurent Sheybani ◽  
Serge Vulliémoz ◽  
Pieter van Mierlo
Keyword(s):  
Information Theory ◽  
Time Series ◽  
Statistical Significance ◽  
Multivariate Time Series ◽  
Surrogate Data ◽  
Essential Information ◽  
Advantages And Disadvantages ◽  
Extensive Evaluation ◽  
Non Linear ◽  
Linear Interactions

The detection of causal effects among simultaneous observations provides knowledge about the underlying network, and is a topic of interests in many scientific areas. Over the years different causality measures have been developed, each with their own advantages and disadvantages. However, an extensive evaluation study is missing. In this work we consider some of the best-known causality measures i.e., cross-correlation, (conditional) Granger causality index (CGCI), partial directed coherence (PDC), directed transfer function (DTF), and partial mutual information on mixed embedding (PMIME). To correct for noise-related spurious connections, each measure (except PMIME) is tested for statistical significance based on surrogate data. The performance of the causality metrics is evaluated on a set of simulation models with distinct characteristics, to assess how well they work in- as well as outside of their “comfort zone.” PDC and DTF perform best on systems with frequency-specific connections, while PMIME is the only one able to detect non-linear interactions. The varying performance depending on the system characteristics warrants the use of multiple measures and comparing their results to avoid errors. Furthermore, lags between coupled variables are inherent to real-world systems and could hold essential information on the network dynamics. They are however often not taken into account and we lack proper tools to estimate them. We propose three new methods for lag estimation in multivariate time series, based on autoregressive modelling and information theory. One of the autoregressive methods and the one based on information theory were able to reliably identify the correct lag value in different simulated systems. However, only the latter was able to maintain its performance in the case of non-linear interactions. As a clinical application, the same methods are also applied on an intracranial recording of an epileptic seizure. The combined knowledge from the causality measures and insights from the simulations, on how these measures perform under different circumstances and when to use which one, allow us to recreate a plausible network of the seizure propagation that supports previous observations of desynchronisation and synchronisation during seizure progression. The lag estimation results show absence of a relationship between connectivity strength and estimated lag values, which contradicts the line of thinking in connectivity shaped by the neuron doctrine.

scholarly journals Global Surface Soil Moisture Dynamics in 1979–2016 Observed from ESA CCI SM Dataset

Water ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 883 ◽  
Author(s):  
Pan ◽  
Wang ◽  
Liu ◽  
Zhao ◽  
Fu
Keyword(s):  
Time Series ◽  
Soil Moisture ◽  
Trend Analysis ◽  
Multiple Time ◽  
Long Time Series ◽  
Seasonal Scale ◽  
Non Linear ◽  
Long Time ◽  
Annual Scale ◽  
Global Surface

Soil moisture (SM) is an important variable for the terrestrial surface system, as its changes greatly affect the global water and energy cycle. The description and understanding of spatiotemporal changes in global soil moisture require long time-series observation. Taking advantage of the European Space Agency (ESA) Climate Change Initiative (CCI) combined SM dataset, this study aims at identifying the non-linear trends of global SM dynamics and their variations at multiple time scales. The distribution of global surface SM changes in 1979–2016 was identified by a non-linear methodology based on a stepwise regression at the annual and seasonal scales. On the annual scale, significant changes have taken place in about one third of the lands, in which nonlinear trends account for 48.13%. At the seasonal scale, the phenomenon that “wet season get wetter, and dry season get dryer” is found this study via hemispherical SM trend analysis at seasonal scale. And, the changes in seasonal SM are more pronounced (change rate at seasonal scales is about 5 times higher than that at annual scale) and the areas seeing significant changes cover a larger surface. Seasonal SM fluctuations distributed in southwestern China, central North America and southern Africa, are concealed at the annual scale. Overall, non-linear trend analysis at multiple time scale has revealed more complex dynamics for these long time series of SM.

scholarly journals A non-linear Granger causality framework to investigate climate–vegetation dynamics

2016 ◽  
Author(s):  
Christina Papagiannopoulou ◽  
Diego G. Miralles ◽  
Niko E. C. Verhoest ◽  
Wouter A. Dorigo ◽  
Willem Waegeman
Keyword(s):  
Time Series ◽  
Granger Causality ◽  
Vegetation Dynamics ◽  
Global Climate ◽  
Multivariate Time Series ◽  
Predictive Modelling ◽  
Experimental Results ◽  
Causality Analysis ◽  
Climate Data ◽  
Non Linear

Abstract. Satellite Earth observation has led to the creation of global climate data records of many important environmental and climatic variables. These take the form of multivariate time series with different spatial and temporal resolutions. Data of this kind provide new means to unravel the influence of climate on vegetation dynamics. However, as advocated in this article, existing statistical methods are often too simplistic to represent complex climate–vegetation relationships due to the assumption of linearity of these relationships. Therefore, as an extension of linear Granger causality analysis, we present a novel non-linear framework consisting of several components, such as data collection from various databases, time series decomposition techniques, feature construction methods and predictive modelling by means of random forests. Experimental results on global data sets indicate that with this framework it is possible to detect non-linear patterns that are much less visible with traditional Granger causality methods. In addition, we also discuss extensive experimental results that highlight the importance of considering the non-linear aspect of climate–vegetation dynamics.

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