scholarly journals Quantifying Statistical Interdependence by Message Passing on Graphs—Part I: One-Dimensional Point Processes

2009 ◽  
Vol 21 (8) ◽  
pp. 2152-2202 ◽  
Author(s):  
J. Dauwels ◽  
F. Vialatte ◽  
T. Weber ◽  
A. Cichocki
Keyword(s):  
Time Series ◽  
Message Passing ◽  
Point Processes ◽  
Pairwise Alignment ◽  
Surrogate Data ◽  
Map Estimation ◽  
One Dimensional ◽  
Novel Approach ◽  
Average Similarity ◽  
Stochastic Event

We present a novel approach to quantify the statistical interdependence of two time series, referred to as stochastic event synchrony (SES). The first step is to extract “events” from the two given time series. The next step is to try to align events from one time series with events from the other. The better the alignment, the more similar the two time series are considered to be. More precisely, the similarity is quantified by the following parameters: time delay, variance of the timing jitter, fraction of noncoincident events, and average similarity of the aligned events. The pairwise alignment and SES parameters are determined by statistical inference. In particular, the SES parameters are computed by maximum a posteriori (MAP) estimation, and the pairwise alignment is obtained by applying the max-product algorithm. This letter deals with one-dimensional point processes; the extension to multidimensional point processes is considered in a companion letter in this issue. By analyzing surrogate data, we demonstrate that SES is able to quantify both timing precision and event reliability more robustly than classical measures can. As an illustration, neuronal spike data generated by the Morris-Lecar neuron model are considered.

scholarly journals Quantifying Statistical Interdependence by Message Passing on Graphs—Part II: Multidimensional Point Processes

2009 ◽  
Vol 21 (8) ◽  
pp. 2203-2268 ◽  
Author(s):  
J. Dauwels ◽  
F. Vialatte ◽  
T. Weber ◽  
T. Musha ◽  
A. Cichocki
Keyword(s):  
Time Series ◽  
Message Passing ◽  
Point Processes ◽  
Graphical Model ◽  
Combinatorial Problem ◽  
Pairwise Alignment ◽  
Surrogate Data ◽  
Multidimensional Case ◽  
Inference Problem ◽  
One Dimensional

Stochastic event synchrony is a technique to quantify the similarity of pairs of signals. First, events are extracted from the two given time series. Next, one tries to align events from one time series with events from the other. The better the alignment, the more similar the two time series are considered to be. In Part I, the companion letter in this issue, one-dimensional events are considered; this letter concerns multidimensional events. Although the basic idea is similar, the extension to multidimensional point processes involves a significantly more difficult combinatorial problem and therefore is nontrivial. Also in the multidimensional case, the problem of jointly computing the pairwise alignment and SES parameters is cast as a statistical inference problem. This problem is solved by coordinate descent, more specifically, by alternating the following two steps: (1) estimate the SES parameters from a given pairwise alignment; (2) with the resulting estimates, refine the pairwise alignment. The SES parameters are computed by maximum a posteriori (MAP) estimation (step 1), in analogy to the one-dimensional case. The pairwise alignment (step 2) can no longer be obtained through dynamic programming, since the state space becomes too large. Instead it is determined by applying the max-product algorithm on a cyclic graphical model. In order to test the robustness and reliability of the SES method, it is first applied to surrogate data. Next, it is applied to detect anomalies in EEG synchrony of mild cognitive impairment (MCI) patients. Numerical results suggest that SES is significantly more sensitive to perturbations in EEG synchrony than a large variety of classical synchrony measures.

scholarly journals Quantifying Statistical Interdependence, Part III: N > 2 Point Processes

2012 ◽  
Vol 24 (2) ◽  
pp. 408-454 ◽  
Author(s):  
Justin Dauwels ◽  
Theophane Weber ◽  
François Vialatte ◽  
Toshimitsu Musha ◽  
Andrzej Cichocki
Keyword(s):  
Time Series ◽  
Point Processes ◽  
Synthetic Data ◽  
Similarity Measures ◽  
Map Estimation ◽  
One Dimensional ◽  
Linear Integer Programming ◽  
The Given ◽  
Stochastic Event ◽  
Alignment Step

Stochastic event synchrony (SES) is a recently proposed family of similarity measures. First, “events” are extracted from the given signals; next, one tries to align events across the different time series. The better the alignment, the more similar the N time series are considered to be. The similarity measures quantify the reliability of the events (the fraction of “nonaligned” events) and the timing precision. So far, SES has been developed for pairs of one-dimensional (Part I) and multidimensional (Part II) point processes. In this letter (Part III), SES is extended from pairs of signals to N > 2 signals. The alignment and SES parameters are again determined through statistical inference, more specifically, by alternating two steps: (1) estimating the SES parameters from a given alignment and (2), with the resulting estimates, refining the alignment. The SES parameters are computed by maximum a posteriori (MAP) estimation (step 1), in analogy to the pairwise case. The alignment (step 2) is solved by linear integer programming. In order to test the robustness and reliability of the proposed N-variate SES method, it is first applied to synthetic data. We show that N-variate SES results in more reliable estimates than bivariate SES. Next N-variate SES is applied to two problems in neuroscience: to quantify the firing reliability of Morris-Lecar neurons and to detect anomalies in EEG synchrony of patients with mild cognitive impairment. Those problems were also considered in Parts I and II, respectively. In both cases, the N-variate SES approach yields a more detailed analysis.

Wavelet analysis of scaling properties of gastric electrical activity

2006 ◽  
Vol 101 (5) ◽  
pp. 1425-1431 ◽  
Author(s):  
Bruce J. West ◽  
Artur Maciejewski ◽  
Miroslaw Latka ◽  
Tadeusz Sebzda ◽  
Zbigniew Swierczynski ◽  
...  
Keyword(s):  
Time Series ◽  
Systemic Sclerosis ◽  
Surrogate Data ◽  
Long Term Memory ◽  
Wavelet Coefficients ◽  
Healthy Individuals ◽  
Scaling Properties ◽  
Statistical Fluctuations ◽  
Novel Approach ◽  
Scaling Index

We present a novel approach to the analysis of fluctuations in human myoelectrical gastric activity measured noninvasively from the surface of the abdomen. The time intervals between successive maxima of the wavelet transformed quasi-periodic electrogastrographic waveform define the gastric rate variability (GRV) time series. By using the method of average wavelet coefficients, the statistical fluctuations in the GRV signal in healthy individuals are determined to scale in time. Such scaling was previously found in a variety of physiological phenomena, all of which support the hypothesis that physiological dynamics utilize fractal time series. We determine the scaling index in a cohort of 17 healthy individuals to be 0.80 ± 0.14, which compared with a set of surrogate data is found to be significant at the level P < 0.01. We also determined that the dynamical pattern, so evident in the spectrum of average wavelet coefficients of the GRV time series of healthy individuals, is significantly reduced in a cohort of systemic sclerosis patients having a scaling index 0.64 ± 0.17. These results imply that the long-term memory in GRV time series is significantly reduced from healthy individuals to those with systemic sclerosis. Consequently, this disease degrades the complexity of the underlying gastrointestinal control system and this degradation is manifest in the loss of scaling in the GRV time series.

scholarly journals Evaluating the performance of multivariate indicators of resilience loss

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Els Weinans ◽  
Rick Quax ◽  
Egbert H. van Nes ◽  
Ingrid A. van de Leemput
Keyword(s):  
Time Series ◽  
Complex Systems ◽  
Multivariate Time Series ◽  
Tipping Points ◽  
Physical And Mental Health ◽  
One Dimensional ◽  
Slowing Down ◽  
The Past ◽  
Technological Developments ◽  
Resilience Indicators

AbstractVarious complex systems, such as the climate, ecosystems, and physical and mental health can show large shifts in response to small changes in their environment. These ‘tipping points’ are notoriously hard to predict based on trends. However, in the past 20 years several indicators pointing to a loss of resilience have been developed. These indicators use fluctuations in time series to detect critical slowing down preceding a tipping point. Most of the existing indicators are based on models of one-dimensional systems. However, complex systems generally consist of multiple interacting entities. Moreover, because of technological developments and wearables, multivariate time series are becoming increasingly available in different fields of science. In order to apply the framework of resilience indicators to multivariate time series, various extensions have been proposed. Not all multivariate indicators have been tested for the same types of systems and therefore a systematic comparison between the methods is lacking. Here, we evaluate the performance of the different multivariate indicators of resilience loss in different scenarios. We show that there is not one method outperforming the others. Instead, which method is best to use depends on the type of scenario the system is subject to. We propose a set of guidelines to help future users choose which multivariate indicator of resilience is best to use for their particular system.

scholarly journals Enhancing Wind Turbine Power Forecast via Convolutional Neural Network

Electronics ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 261
Author(s):  
Tianyang Liu ◽  
Zunkai Huang ◽  
Li Tian ◽  
Yongxin Zhu ◽  
Hui Wang ◽  
...  
Keyword(s):  
Time Series ◽  
Wind Speed ◽  
Wind Turbine ◽  
Wind Power ◽  
Rapid Development ◽  
Superior Performance ◽  
Learning Platform ◽  
Novel Approach ◽  
Wind Power Forecast ◽  
Transformation Methods

The rapid development in wind power comes with new technical challenges. Reliable and accurate wind power forecast is of considerable significance to the electricity system’s daily dispatching and production. Traditional forecast methods usually utilize wind speed and turbine parameters as the model inputs. However, they are not sufficient to account for complex weather variability and the various wind turbine features in the real world. Inspired by the excellent performance of convolutional neural networks (CNN) in computer vision, we propose a novel approach to predicting short-term wind power by converting time series into images and exploit a CNN to analyze them. In our approach, we first propose two transformation methods to map wind speed and precipitation data time series into image matrices. After integrating multi-dimensional information and extracting features, we design a novel CNN framework to forecast 24-h wind turbine power. Our method is implemented on the Keras deep learning platform and tested on 10 sets of 3-year wind turbine data from Hangzhou, China. The superior performance of the proposed method is demonstrated through comparisons using state-of-the-art techniques in wind turbine power forecasting.

scholarly journals A Process-Oriented Approach to Identify Evolutions of Sea Surface Temperature Anomalies with a Time-Series of a Raster Dataset

2021 ◽  
Vol 10 (8) ◽  
pp. 500
Author(s):  
Lianwei Li ◽  
Yangfeng Xu ◽  
Cunjin Xue ◽  
Yuxuan Fu ◽  
Yuanyu Zhang
Keyword(s):  
Time Series ◽  
Surface Temperature ◽  
Sea Surface Temperature ◽  
Global Climate ◽  
Sea Surface ◽  
Temperature Anomalies ◽  
Global Climate Changes ◽  
Space And Time ◽  
Novel Approach ◽  
Sea Surface Temperature Anomalies

It is important to consider where, when, and how the evolution of sea surface temperature anomalies (SSTA) plays significant roles in regional or global climate changes. In the comparison of where and when, there is a great challenge in clearly describing how SSTA evolves in space and time. In light of the evolution from generation, through development, and to the dissipation of SSTA, this paper proposes a novel approach to identifying an evolution of SSTA in space and time from a time-series of a raster dataset. This method, called PoAIES, includes three key steps. Firstly, a cluster-based method is enhanced to explore spatiotemporal clusters of SSTA, and each cluster of SSTA at a time snapshot is taken as a snapshot object of SSTA. Secondly, the spatiotemporal topologies of snapshot objects of SSTA at successive time snapshots are used to link snapshot objects of SSTA into an evolution object of SSTA, which is called a process object. Here, a linking threshold is automatically determined according to the overlapped areas of the snapshot objects, and only those snapshot objects that meet the specified linking threshold are linked together into a process object. Thirdly, we use a graph-based model to represent a process object of SSTA. A node represents a snapshot object of SSTA, and an edge represents an evolution between two snapshot objects. Using a number of child nodes from an edge’s parent node and a number of parent nodes from the edge’s child node, a type of edge (an evolution relationship) is identified, which shows its development, splitting, merging, or splitting/merging. Finally, an experiment on a simulated dataset is used to demonstrate the effectiveness and the advantages of PoAIES, and a real dataset of satellite-SSTA is used to verify the rationality of PoAIES with the help of ENSO’s relevant knowledge, which may provide new references for global change research.

scholarly journals Nonlinear analysis of magnetospheric data Part I. Geometric characteristics of the AE index time series and comparison with nonlinear surrogate data

1999 ◽  
Vol 6 (1) ◽  
pp. 51-65 ◽  
Author(s):  
G. P. Pavlos ◽  
M. A. Athanasiu ◽  
D. Kugiumtzis ◽  
N. Hatzigeorgiu ◽  
A. G. Rigas ◽  
...  
Keyword(s):  
Time Series ◽  
State Space ◽  
Null Hypothesis ◽  
Surrogate Data ◽  
Statistical Testing ◽  
Geometrical Parameters ◽  
Geometric Characteristics ◽  
Geometrical Characteristics ◽  
Ae Index ◽  
Index Time Series

Abstract. A long AE index time series is used as a crucial magnetospheric quantity in order to study the underlying dynainics. For this purpose we utilize methods of nonlinear and chaotic analysis of time series. Two basic components of this analysis are the reconstruction of the experimental tiine series state space trajectory of the underlying process and the statistical testing of an null hypothesis. The null hypothesis against which the experimental time series are tested is that the observed AE index signal is generated by a linear stochastic signal possibly perturbed by a static nonlinear distortion. As dis ' ' ating statistics we use geometrical characteristics of the reconstructed state space (Part I, which is the work of this paper) and dynamical characteristics (Part II, which is the work a separate paper), and "nonlinear" surrogate data, generated by two different techniques which can mimic the original (AE index) signal. lie null hypothesis is tested for geometrical characteristics which are the dimension of the reconstructed trajectory and some new geometrical parameters introduced in this work for the efficient discrimination between the nonlinear stochastic surrogate data and the AE index. Finally, the estimated geometric characteristics of the magnetospheric AE index present new evidence about the nonlinear and low dimensional character of the underlying magnetospheric dynamics for the AE index.

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