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 Data Augmentation with Suboptimal Warping for Time-Series Classification

Sensors ◽  
2019 ◽  
Vol 20 (1) ◽  
pp. 98 ◽  
Author(s):  
Krzysztof Kamycki ◽  
Tomasz Kapuscinski ◽  
Mariusz Oszust
Keyword(s):  
Time Series ◽  
Data Augmentation ◽  
Nearest Neighbor ◽  
Multivariate Time Series ◽  
Metric Learning ◽  
Classification Performance ◽  
Training Dataset ◽  
Time Series Classification ◽  
Extensive Evaluation ◽  
The Impact

In this paper, a novel data augmentation method for time-series classification is proposed. In the introduced method, a new time-series is obtained in warped space between suboptimally aligned input examples of different lengths. Specifically, the alignment is carried out constraining the warping path and reducing its flexibility. It is shown that the resultant synthetic time-series can form new class boundaries and enrich the training dataset. In this work, the comparative evaluation of the proposed augmentation method against related techniques on representative multivariate time-series datasets is presented. The performance of methods is examined using the nearest neighbor classifier with the dynamic time warping (NN-DTW), LogDet divergence-based metric learning with triplet constraints (LDMLT), and the recently introduced time-series cluster kernel (NN-TCK). The impact of the augmentation on the classification performance is investigated, taking into account entire datasets and cases with a small number of training examples. The extensive evaluation reveals that the introduced method outperforms related augmentation algorithms in terms of the obtained classification accuracy.

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 Normalized Multivariate Time Series Causality Analysis and Causal Graph Reconstruction

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 679
Author(s):  
X. San Liang
Keyword(s):  
Time Series ◽  
Data Science ◽  
Statistical Significance ◽  
Multivariate Time Series ◽  
Theoretical Development ◽  
Causality Analysis ◽  
Causal Inferences ◽  
Signal Ratio ◽  
Causal Graph ◽  
Causal Graphs

Causality analysis is an important problem lying at the heart of science, and is of particular importance in data science and machine learning. An endeavor during the past 16 years viewing causality as a real physical notion so as to formulate it from first principles, however, seems to have gone unnoticed. This study introduces to the community this line of work, with a long-due generalization of the information flow-based bivariate time series causal inference to multivariate series, based on the recent advance in theoretical development. The resulting formula is transparent, and can be implemented as a computationally very efficient algorithm for application. It can be normalized and tested for statistical significance. Different from the previous work along this line where only information flows are estimated, here an algorithm is also implemented to quantify the influence of a unit to itself. While this forms a challenge in some causal inferences, here it comes naturally, and hence the identification of self-loops in a causal graph is fulfilled automatically as the causalities along edges are inferred. To demonstrate the power of the approach, presented here are two applications in extreme situations. The first is a network of multivariate processes buried in heavy noises (with the noise-to-signal ratio exceeding 100), and the second a network with nearly synchronized chaotic oscillators. In both graphs, confounding processes exist. While it seems to be a challenge to reconstruct from given series these causal graphs, an easy application of the algorithm immediately reveals the desideratum. Particularly, the confounding processes have been accurately differentiated. Considering the surge of interest in the community, this study is very timely.

scholarly journals A comparative study on chaoticity of equatorial/low latitude ionosphere over Indian subcontinent during geomagnetically quiet and disturbed periods

2010 ◽  
Vol 17 (6) ◽  
pp. 765-776 ◽  
Author(s):  
K. Unnikrishnan
Keyword(s):  
Time Series ◽  
Prediction Error ◽  
Correlation Dimension ◽  
Linear Prediction ◽  
Indian Subcontinent ◽  
Surrogate Data ◽  
Chaotic Behaviour ◽  
Quiet Period ◽  
Nonlinear Prediction ◽  
Non Linear

Abstract. In the present study, the latitudinal aspect of chaotic behaviour of ionosphere during quiet and storm periods are analyzed and compared by using GPS TEC time series measured at equatorial trough, crest and outside crest stations over Indian subcontinent, by employing the chaotic quantifiers like Lyapunov exponent (LE), correlation dimension (CD), entropy and nonlinear prediction error (NPE). It is observed that the values of LE are low for storm periods compared to those of quiet periods for all the stations considered here. The lowest value of LE is observed at the trough station, Agatti (2.38° N, Geomagnetically), and highest at crest station, Mumbai (10.09° N, Geomagnetically) for both quiet and storm periods. The values of correlation dimension computed for TEC time series are in the range 2.23–2.74 for quiet period, which indicate that equatorial ionosphere may be described with three variables during quiet period. But the crest station Mumbai shows a higher value of CD (3.373) during storm time, which asserts that four variables are necessary to describe the system during storm period. The values of non linear prediction error (NPE) are lower for Agatti (2.38° N, Geomagnetically) and Jodhpur (18.3° N, Geomagnetically), during storm period, compared to those of quiet period, mainly because of the predominance of non linear aspects during storm periods The surrogate data test is carried out and on the basis of the significance of difference of the original data and surrogates for various aspects, the surrogate data test rejects the null hypothesis that the time series of TEC during storm and quiet times represent a linear stochastic process. It is also observed that using state space model, detrended TEC can be predicted, which reasonably reproduces the observed data. Based on the values of the above quantifiers, the features of chaotic behaviour of equatorial trough crest and outside the crest regions of ionosphere during geomagnetically quiet and disturbed periods are briefly discussed.

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.

Cancer's role in chemotherapy-induced neuropathy.

2020 ◽  
Vol 38 (15_suppl) ◽  
pp. e24064-e24064
Author(s):  
Stephen Nick Housley ◽  
Paul Nardelli ◽  
Allison B. Wang ◽  
Ann Marie Flores ◽  
Eric J. Perreault ◽  
...  
Keyword(s):  
Error Rate ◽  
Statistical Significance ◽  
Sensory Neuropathy ◽  
Experimental Models ◽  
Control Treatment ◽  
Rat Colon ◽  
Neuronal Signaling ◽  
Non Linear ◽  
Linear Interactions

e24064 Background: For the constellation of neurological disorders known as chemotherapy-induced neuropathy, mechanistic understanding, and treatment remain deficient. This might be due to the fact that studies on the effects of chemotherapies on the nervous system have utilized experimental models that exclude cancer perhaps due to the presumption that chemotherapy alone explains the neuropathology. However, the convergence of cancer and chemotherapy on the same biological processes seems likely to yield non-linear interactions. This led us to hypothesize that clinically relevant neuropathy emerges from codependent actions of cancer and chemotherapy. Methods: We established a clinically-relevant animal model of chronic sensory neuropathy in rats with cancer (adenomatous polyposis coli in rat colon: Apc+/Pirc) and age-matched animals without cancer ( ApcWT) that were randomly assigned to receive a human-scaled course of oxaliplatin (OX) or control treatment (4 groups). We quantified behavioral deficits during precision ladder walking, a validated measure of locomotor performance. Neuronal signaling was measured during terminal in vivo experiments to examine the response of sensory neurons to physiologically-relevant stimuli. We defined statistical significance as when 95% of a highest density interval (HDI) of posterior probabilities do not overlap (hierarchical Bayesian modeling). Results: Apc+/Pirc+OX (n = 11) rats exhibited significantly higher error rate (19.2±5.6%, 95%HDI) during precision ladder walking in comparison to ApcWT+control (2.4±2.7%: n = 9) or Apc+/Pirc +control (2.5±2.9%: n = 7) and significantly exceeded the error rate observed in animals treated with OX alone (8.4±3.1%: n = 10). In contrast to the observations in all other groups, we found drastically impaired neuronal signaling in Apc+/Pirc+OX rats which manifested as significantly reduced sensitivity and attenuated static and dynamic firing patterns (95%HDI). Conclusions: We present the first evidence that chronic neuropathy cannot be explained by the effects of chemotherapy alone but instead depend on non-linear interactions between cancer and chemotherapy. This understanding is a prerequisite for developing meaningful treatment or prevention of neuropathy.

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.

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