Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction

2006 ◽  
Vol 1 (1) ◽  
pp. 111-114 ◽  
Author(s):  
Hong-guang Ma ◽  
Chong-zhao Han
Keyword(s):  
Phase Space ◽  
Delay Time ◽  
Phase Space Reconstruction ◽  
Embedding Dimension ◽  
Selection Of

scholarly journals Parameter Selection for Phase Space Reconstruction in Hydrological Series and Rationality Analysis of its Chaotic Characteristics

10.29007/2fb8 ◽  
2018 ◽  
Author(s):  
Hongyan Li ◽  
Shanshan Bao ◽  
Yunqing Xuan
Keyword(s):  
Time Series ◽  
Phase Space ◽  
River Basin ◽  
Delay Time ◽  
Phase Space Reconstruction ◽  
Sequence Length ◽  
Rainfall Time Series ◽  
Embedding Dimension ◽  
Characteristic Index ◽  
Runoff Series

This study performed a rationality analysis of the delay time and embedding dimension value during phase space reconstruction in hydrological series and the effect on their chaotic characteristics. Using a monthly average runoff time series from the Ayanqian station (upstream) and the Jiangqiao station (midstream) in the Nen River Basin, we reached the following regularity conclusions. 1 Based on the flood season (4 months) in the Nen River Basin, we can deduce that the correlation sequence length for the runoff is 4~5 months, i.e., the delay time =3 or 4 is a reasonable choice. 2 Learn from the predictability experiment results for the monthly rainfall time series, we know that the calculation results of the G-P algorithm for the dimension of runoff series for the Nen River Basin are reasonable, i.e., the embedding dimension is no more than seven. 3 the most suitable parameters for the phase space reconstruction and its chaotic characteristic index in the Nen River Basin are as follows: delay time = 3~4, embedding dimension = 6~7, correlation dimension = 2.90~3.00, maximum Lyapunov index = 0.24~0.32, and the forecast time is 3~4 months.

Selection of proper embedding dimension in phase space reconstruction of speech signals

2000 ◽  
Vol 17 (2) ◽  
pp. 161-169 ◽  
Author(s):  
Jiayu Lin ◽  
Zhiping Huang ◽  
Yueke Wang ◽  
Zhenken Shen
Keyword(s):  
Phase Space ◽  
Phase Space Reconstruction ◽  
Speech Signals ◽  
Embedding Dimension ◽  
Selection Of

scholarly journals Selection of Phase Space Reconstruction Parameters for EMG Signals of the Uterus

2016 ◽  
Vol 47 (1) ◽  
pp. 47-59 ◽  
Author(s):  
Ewelina Brzozowska ◽  
Marta Borowska
Keyword(s):  
Phase Space ◽  
Contractile Activity ◽  
Digital Signal ◽  
Phase Space Reconstruction ◽  
Original Signal ◽  
Embedding Dimension ◽  
Biological Time ◽  
Uterine Muscle ◽  
Muscle Contractile ◽  
Selection Of

Abstract Biological time series have a finite number of samples with noise included in them. Because of this fact, it is not possible to reconstruct phase space in an ideal manner. One kind of biomedical signals are electrohisterographical (EHG) datasets, which represent uterine muscle contractile activity. In the process of phase space reconstruction, the most important thing is suitable choice of the method for calculating the time delay τ and embedding dimension d, which will reliably reconstruct the original signal. The parameters used in digital signal processing are key to arranging adequate parameters of the analysed attractor embedded in the phase space. The aim of this paper is to present a method employed for phase space reconstruction for EHG signals that will make it possible for their further analysis to be carried out.

A Study On Methods for Determining Phase Space Reconstruction Parameters

2021 ◽  
Author(s):  
Shihui Lang ◽  
Zhu Hua ◽  
Guodong Sun ◽  
Yu Jiang ◽  
Chunling Wei
Keyword(s):  
Time Delay ◽  
Phase Space ◽  
Correlation Dimension ◽  
Nearest Neighbor ◽  
Correlation Method ◽  
Phase Space Reconstruction ◽  
Lorenz Attractor ◽  
Embedding Dimension ◽  
Phase Trajectories ◽  
Auto Correlation

Abstract Several pairs of algorithms were used to determine the phase space reconstruction parameters to analyze the dynamic characteristics of chaotic time series. The reconstructed phase trajectories were compared with the original phase trajectories of the Lorenz attractor, Rössler attractor, and Chens attractor to obtain the optimum method for determining the phase space reconstruction parameters with high precision and efficiency. The research results show that the false nearest neighbor method and the complex auto-correlation method provided the best results. The saturated embedding dimension method based on the saturated correlation dimension method is proposed to calculate the time delay. Different time delays are obtained by changing the embedding dimension parameters of the complex auto-correlation method. The optimum time delay occurs at the point where the time delay is stable. The validity of the method is verified through combing the application of correlation dimension, showing that the proposed method is suitable for the effective determination of the phase space reconstruction parameters.

scholarly journals Hybrid prediction method of ECG signals based on VMD, PSR, and RBF neural network

2020 ◽  
Author(s):  
Fuying Huang ◽  
Tuanfa Qin ◽  
Limei Wang ◽  
Haibin Wan
Keyword(s):  
Neural Network ◽  
Phase Space ◽  
Delay Time ◽  
Prediction Accuracy ◽  
Rbf Neural Network ◽  
Prediction Method ◽  
Prediction Methods ◽  
Embedding Dimension ◽  
Ecg Signals ◽  
Ecg Data

Abstract Background: It is significant for doctors and body area networks (BANs) to predict ECG signals accurately. At present, the prediction accuracy of many existing ECG prediction methods is generally low. In order to improve the prediction accuracy of ECG signals in BANs, a hybrid prediction method of ECG signals is proposed in this paper. Methods: The proposed prediction method combines variational mode decomposition (VMD), phase space reconstruction (PSR), and a radial basis function (RBF) neural network. First, the embedding dimension and delay time of PSR are calculated according to the trained set of ECG data. Second, the ECG data are decomposed into several intrinsic mode functions (IMFs). Third, the phase space of each IMF is reconstructed according to the embedding dimension and the delay time. Fourth, an RBF neural network is established and each IMF is predicted by the network. Finally, the prediction results of all IMFs are added to realize the final prediction result. Results: To evaluate the prediction performance of the proposed method, simulation experiments are carried out on ECG data from the MIT-BIH Arrhythmia Database. The experimental results show that the prediction index RMSE (root mean square error) of the proposed method is only 10-3 magnitude and that of some traditional prediction methods is 10-2 magnitude.Conclusions: Compared with some traditional prediction methods, the proposed method improves the prediction accuracy of ECG signals obviously.

scholarly journals Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 221
Author(s):  
Mariano Matilla-García ◽  
Isidro Morales ◽  
Jose Miguel Rodríguez ◽  
Manuel Ruiz Marín
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Phase Space ◽  
Mutual Information ◽  
Phase Space Reconstruction ◽  
Chaotic Time Series ◽  
Optimal Time ◽  
Embedding Dimension ◽  
Simple Method ◽  
Correlation Integral

The modeling and prediction of chaotic time series require proper reconstruction of the state space from the available data in order to successfully estimate invariant properties of the embedded attractor. Thus, one must choose appropriate time delay τ∗ and embedding dimension p for phase space reconstruction. The value of τ∗ can be estimated from the Mutual Information, but this method is rather cumbersome computationally. Additionally, some researchers have recommended that τ∗ should be chosen to be dependent on the embedding dimension p by means of an appropriate value for the time delay τw=(p−1)τ∗, which is the optimal time delay for independence of the time series. The C-C method, based on Correlation Integral, is a method simpler than Mutual Information and has been proposed to select optimally τw and τ∗. In this paper, we suggest a simple method for estimating τ∗ and τw based on symbolic analysis and symbolic entropy. As in the C-C method, τ∗ is estimated as the first local optimal time delay and τw as the time delay for independence of the time series. The method is applied to several chaotic time series that are the base of comparison for several techniques. The numerical simulations for these systems verify that the proposed symbolic-based method is useful for practitioners and, according to the studied models, has a better performance than the C-C method for the choice of the time delay and embedding dimension. In addition, the method is applied to EEG data in order to study and compare some dynamic characteristics of brain activity under epileptic episodes

Determining embedding dimension for phase-space reconstruction using a geometrical construction

1992 ◽  
Vol 45 (6) ◽  
pp. 3403-3411 ◽  
Author(s):  
Matthew B. Kennel ◽  
Reggie Brown ◽  
Henry D. I. Abarbanel
Keyword(s):  
Phase Space ◽  
Phase Space Reconstruction ◽  
Embedding Dimension ◽  
Geometrical Construction
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