scholarly journals A New Recurrence-Network-Based Time Series Analysis Approach for Characterizing System Dynamics

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 45 ◽  
Author(s):  
Guangyu Yang ◽  
Daolin Xu ◽  
Haicheng Zhang
Keyword(s):  
Time Series ◽  
Ventricular Tachycardia ◽  
Dynamical Systems ◽  
Healthy Subjects ◽  
Additive Noise ◽  
High Dimensional ◽  
Analysis Method ◽  
Decline Rate ◽  
Low Dimensional ◽  
Edge Similarity

In this paper, a novel analysis method based on recurrence networks is proposed to characterize the evolution of dynamical systems. Through phase space reconstruction, a time series was transformed into a high-dimensional recurrence network and a corresponding low-dimensional recurrence network, respectively. Then, two appropriate statistics, the correlation coefficient of node degrees (CCND) and the edge similarity, were proposed to unravel the evolution properties of the considered signal. Through the investigation of the time series with distinct dynamics, different patterns in the decline rate of the CCND at different network dimensions were observed. Interestingly, an exponential scaling emerged in the CCND analysis for the chaotic time series. Moreover, it was demonstrated that the edge similarity can further characterize dynamical systems and provide detailed information on the studied time series. A method based on the fluctuation of edge similarities for neighboring edge groups was proposed to determine the number of groups that the edges should be partitioned into. Through the analysis of chaotic series corrupted by noise, it was demonstrated that both the CCND and edge similarity derived from different time series are robust under additive noise. Finally, the application of the proposed method to ventricular time series showed its effectiveness in differentiating healthy subjects from ventricular tachycardia (VT) patients.

scholarly journals LSTM-Guided Coaching Assistant for Table Tennis Practice

Sensors ◽  
2018 ◽  
Vol 18 (12) ◽  
pp. 4112 ◽  
Author(s):  
Se-Min Lim ◽  
Hyeong-Cheol Oh ◽  
Jaein Kim ◽  
Juwon Lee ◽  
Jooyoung Park
Keyword(s):  
Time Series ◽  
State Space ◽  
Time Series Data ◽  
State Space Model ◽  
Skill Assessment ◽  
Series Data ◽  
High Dimensional ◽  
Table Tennis ◽  
Space Model ◽  
Low Dimensional

Recently, wearable devices have become a prominent health care application domain by incorporating a growing number of sensors and adopting smart machine learning technologies. One closely related topic is the strategy of combining the wearable device technology with skill assessment, which can be used in wearable device apps for coaching and/or personal training. Particularly pertinent to skill assessment based on high-dimensional time series data from wearable sensors is classifying whether a player is an expert or a beginner, which skills the player is exercising, and extracting some low-dimensional representations useful for coaching. In this paper, we present a deep learning-based coaching assistant method, which can provide useful information in supporting table tennis practice. Our method uses a combination of LSTM (Long short-term memory) with a deep state space model and probabilistic inference. More precisely, we use the expressive power of LSTM when handling high-dimensional time series data, and state space model and probabilistic inference to extract low-dimensional latent representations useful for coaching. Experimental results show that our method can yield promising results for characterizing high-dimensional time series patterns and for providing useful information when working with wearable IMU (Inertial measurement unit) sensors for table tennis coaching.

scholarly journals Extracting Low-Dimensional Latent Structure from Time Series in the Presence of Delays

2015 ◽  
Vol 27 (9) ◽  
pp. 1825-1856 ◽  
Author(s):  
Karthik C. Lakshmanan ◽  
Patrick T. Sadtler ◽  
Elizabeth C. Tyler-Kabara ◽  
Aaron P. Batista ◽  
Byron M. Yu
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Motor Cortex ◽  
Dimensionality Reduction ◽  
Gaussian Process ◽  
Latent Variables ◽  
Time Delays ◽  
High Dimensional ◽  
Latent Space ◽  
Low Dimensional

Noisy, high-dimensional time series observations can often be described by a set of low-dimensional latent variables. Commonly used methods to extract these latent variables typically assume instantaneous relationships between the latent and observed variables. In many physical systems, changes in the latent variables manifest as changes in the observed variables after time delays. Techniques that do not account for these delays can recover a larger number of latent variables than are present in the system, thereby making the latent representation more difficult to interpret. In this work, we introduce a novel probabilistic technique, time-delay gaussian-process factor analysis (TD-GPFA), that performs dimensionality reduction in the presence of a different time delay between each pair of latent and observed variables. We demonstrate how using a gaussian process to model the evolution of each latent variable allows us to tractably learn these delays over a continuous domain. Additionally, we show how TD-GPFA combines temporal smoothing and dimensionality reduction into a common probabilistic framework. We present an expectation/conditional maximization either (ECME) algorithm to learn the model parameters. Our simulations demonstrate that when time delays are present, TD-GPFA is able to correctly identify these delays and recover the latent space. We then applied TD-GPFA to the activity of tens of neurons recorded simultaneously in the macaque motor cortex during a reaching task. TD-GPFA is able to better describe the neural activity using a more parsimonious latent space than GPFA, a method that has been used to interpret motor cortex data but does not account for time delays. More broadly, TD-GPFA can help to unravel the mechanisms underlying high-dimensional time series data by taking into account physical delays in the system.

Bayesian recurrent neural network as a tool for reconstructing dynamical systems from multidimensional data

2020 ◽  
Author(s):  
Alexander Feigin ◽  
Aleksei Seleznev ◽  
Dmitry Mukhin ◽  
Andrey Gavrilov ◽  
Evgeny Loskutov
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Cost Function ◽  
Recurrent Neural Network ◽  
Bayesian Optimization ◽  
Data Driven ◽  
High Dimensional ◽  
Model Learning ◽  
Low Dimensional ◽  
The Cost

<p>We suggest a new method for construction of data-driven dynamical models from observed multidimensional time series. The method is based on a recurrent neural network (RNN) with specific structure, which allows for the joint reconstruction of both a low-dimensional embedding for dynamical components in the data and an operator describing the low-dimensional evolution of the system. The key link of the method is a Bayesian optimization of both model structure and the hypothesis about the data generating law, which is needed for constructing the cost function for model learning.  The form of the model we propose allows us to construct a stochastic dynamical system of moderate dimension that copies dynamical properties of the original high-dimensional system. An advantage of the proposed method is the data-adaptive properties of the RNN model: it is based on the adjustable nonlinear elements and has easily scalable structure. The combination of the RNN with the Bayesian optimization procedure efficiently provides the model with statistically significant nonlinearity and dimension.<br>The method developed for the model optimization aims to detect the long-term connections between system’s states – the memory of the system: the cost-function used for model learning is constructed taking into account this factor. In particular, in the case of absence of interaction between the dynamical component and noise, the method provides unbiased reconstruction of the hidden deterministic system. In the opposite case when the noise has strong impact on the dynamics, the method yield a model in the form of a nonlinear stochastic map determining the Markovian process with memory. Bayesian approach used for selecting both the optimal model’s structure and the appropriate cost function allows to obtain the statistically significant inferences about the dynamical signal in data as well as its interaction with the noise components.<br>Data driven model derived from the relatively short time series of the QG3 model – the high dimensional nonlinear system producing chaotic behavior – is shown be able to serve as a good simulator for the QG3 LFV components. The statistically significant recurrent states of the QG3 model, i.e. the well-known teleconnections in NH, are all reproduced by the model obtained. Moreover, statistics of the residence times of the model near these states is very close to the corresponding statistics of the original QG3 model. These results demonstrate that the method can be useful in modeling the variability of the real atmosphere.</p><p>The work was supported by the Russian Science Foundation (Grant No. 19-42-04121).</p>

DYNAMICAL SYSTEMS AND TESSELATIONS: DETECTING DETERMINISM IN DATA

1991 ◽  
Vol 01 (04) ◽  
pp. 777-794 ◽  
Author(s):  
ALISTAIR I. MEES
Keyword(s):  
Dynamical System ◽  
Time Series ◽  
Dynamical Systems ◽  
State Space ◽  
Scientific Theory ◽  
Invariant Manifolds ◽  
Geometric Information ◽  
Topological Information ◽  
Low Dimensional ◽  
Dynamical Information

Data measurements from a dynamical system may be used to build triangulations and tesselations which can — at least when the system has relatively low-dimensional attractors or invariant manifolds — give topological, geometric and dynamical information about the system. The data may consist of a time series, possibly reconstructed by embedding, or of several such series; transients can be put to good use. The topological information which can be found includes dimension and genus of a manifold containing the state space. Geometric information includes information about folds, branches and other chaos generators. Dynamical information is obtained by using the tesselation to construct a map with stated smoothness properties and having the same dynamics as the data; the resulting dynamical model may be tested in the way that any scientific theory may be tested, by making falsifiable predictions.

scholarly journals Wavelet filtering of chaotic data

2000 ◽  
Vol 7 (1/2) ◽  
pp. 111-116 ◽  
Author(s):  
M. Grzesiak
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Finite Impulse Response ◽  
Gaussian White Noise ◽  
Noisy Data ◽  
Singular Value ◽  
Filter Methods ◽  
Satisfactory Method ◽  
Low Dimensional ◽  
Value Decomposition

Abstract. Satisfactory method of removing noise from experimental chaotic data is still an open problem. Normally it is necessary to assume certain properties of the noise and dynamics, which one wants to extract, from time series. The wavelet based method of denoising of time series originating from low-dimensional dynamical systems and polluted by the Gaussian white noise is considered. Its efficiency is investigated by comparing the correlation dimension of clean and noisy data generated for some well-known dynamical systems. The wavelet method is contrasted with the singular value decomposition (SVD) and finite impulse response (FIR) filter methods.

Information-Theoretic Characterization of Bifurcations in Nonlinear Dynamical Systems With Noise

2013 ◽  
Author(s):  
Navendu S. Patil ◽  
Joseph P. Cusumano
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Nonlinear Dynamical Systems ◽  
Period Doubling ◽  
Entropy Rate ◽  
Series Data ◽  
High Dimensional ◽  
Dimensional System ◽  
Dimensional Manifold ◽  
Low Dimensional

Detecting bifurcations in noisy and/or high-dimensional physical systems is an important problem in nonlinear dynamics. Near bifurcations, the dynamics of even a high dimensional system is typically dominated by its behavior on a low dimensional manifold. Since the system is sensitive to perturbations near bifurcations, they can be detected by looking at the apparent deterministic structure generated by the interaction between the noise and low-dimensional dynamics. We use minimal hidden Markov models built from the noisy time series to quantify this deterministic structure at the period-doubling bifurcations in the two-well forced Duffing oscillator perturbed by noise. The apparent randomness in the system is characterized using the entropy rate of the discrete stochastic process generated by partitioning time series data. We show that as the bifurcation parameter is varied, sharp changes in the statistical complexity and the entropy rate can be used to locate incipient bifurcations.

scholarly journals Multivariate time series prediction of high dimensional data based on deep reinforcement learning

2021 ◽  
Vol 256 ◽  
pp. 02038
Author(s):  
Xin Ji ◽  
Haifeng Zhang ◽  
Jianfang Li ◽  
Xiaolong Zhao ◽  
Shouchao Li ◽  
...  
Keyword(s):  
Time Series ◽  
Reinforcement Learning ◽  
Phase Space ◽  
Time Series Prediction ◽  
Multivariate Time Series ◽  
High Dimensional Data ◽  
Prediction Method ◽  
Conditional Entropy ◽  
High Dimensional ◽  
Low Dimensional

In order to improve the prediction accuracy of high-dimensional data time series, a high-dimensional data multivariate time series prediction method based on deep reinforcement learning is proposed. The deep reinforcement learning method is used to solve the time delay of each variable and mine the data characteristics. According to the principle of maximum conditional entropy, the embedding dimension of the phase space is expanded, and a multivariate time series model of high-dimensional data is constructed. Thus, the conversion of reconstructed coordinates from low-dimensional to high-dimensional can be kept relatively stable. The strong independence and low redundancy of the final reconstructed phase space construct an effective model input vector for multivariate time series forecasting. Numerical experiments of classical multivariable chaotic time series show that the method proposed in this paper has better forecasting effect, which shows the forecasting effectiveness of this method.

Numerical Bifurcation Methods and their Application to Fluid Dynamics: Analysis beyond Simulation

2014 ◽  
Vol 15 (1) ◽  
pp. 1-45 ◽  
Author(s):  
Henk A. Dijkstra ◽  
Fred W. Wubs ◽  
Andrew K. Cliffe ◽  
Eusebius Doedel ◽  
Ioana F. Dragomirescu ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Bifurcation Analysis ◽  
Jacobian Matrix ◽  
Critical Conditions ◽  
High Dimensional ◽  
Tipping Points ◽  
Numerical Bifurcation ◽  
Low Dimensional ◽  
Bifurcation Methods ◽  
Numerical Bifurcation Analysis

AbstractWe provide an overview of current techniques and typical applications of numerical bifurcation analysis in fluid dynamical problems. Many of these problems are characterized by high-dimensional dynamical systems which undergo transitions as parameters are changed. The computation of the critical conditions associated with these transitions, popularly referred to as ‘tipping points’, is important for understanding the transition mechanisms. We describe the two basic classes of methods of numerical bifurcation analysis, which differ in the explicit or implicit use of the Jacobian matrix of the dynamical system. The numerical challenges involved in both methods arementioned and possible solutions to current bottlenecks are given. To demonstrate that numerical bifurcation techniques are not restricted to relatively low-dimensional dynamical systems, we provide several examples of the application of the modern techniques to a diverse set of fluid mechanical problems.

Predicting Time Series from Short-Term High-Dimensional Data

2014 ◽  
Vol 24 (12) ◽  
pp. 1430033 ◽  
Author(s):  
Huanfei Ma ◽  
Tianshou Zhou ◽  
Kazuyuki Aihara ◽  
Luonan Chen
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
High Dimensional Data ◽  
Series Data ◽  
High Dimensional ◽  
Short Term ◽  
Low Dimensional ◽  
Low Dimensional Dynamics ◽  
Term Data

The prediction of future values of time series is a challenging task in many fields. In particular, making prediction based on short-term data is believed to be difficult. Here, we propose a method to predict systems' low-dimensional dynamics from high-dimensional but short-term data. Intuitively, it can be considered as a transformation from the inter-variable information of the observed high-dimensional data into the corresponding low-dimensional but long-term data, thereby equivalent to prediction of time series data. Technically, this method can be viewed as an inverse implementation of delayed embedding reconstruction. Both methods and algorithms are developed. To demonstrate the effectiveness of the theoretical result, benchmark examples and real-world problems from various fields are studied.

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