Recognition of the scale-free interval for calculating the correlation dimension using machine learning from chaotic time series

2021 ◽  
pp. 126563
Author(s):  
Shuang Zhou ◽  
Xingyuan Wang ◽  
Wenjie Zhou ◽  
Chuan Zhang
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Correlation Dimension ◽  
Chaotic Time Series ◽  
Scale Free ◽  
Free Interval

Study on Prediction of Mackey-Glass Chaotic Time Series Using Support Vector Machines

2014 ◽  
Vol 1051 ◽  
pp. 1009-1015 ◽  
Author(s):  
Ya Li Ning ◽  
Xin You Wang ◽  
Xi Ping He
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Support Vector Machines ◽  
Statistical Learning ◽  
Chaotic Time Series ◽  
Support Vector ◽  
Machine Type ◽  
Type Selection ◽  
Vector Machines ◽  
New Generation

Support Vector Machines (SVM), which is a new generation learning method based on advances in statistical learning theory, is characterized by the use of many standard technologies of machine learning such as maximal margin hyperplane, Mercel kernels and the quadratic programming. Because the best performance is obtained in many currently challenging applications, SVM has sustained wide attention, and has been become the standard tools of machine learning and data mining. But as a developing technology, SVM still have some problems and its applications are limited. In this paper, SVM and its applications in chaotic time series including predicting chaotic time series, focus on comparison in regression type selection, and kernel type selection in the same regression machine type.

OPTIMAL RECONSTRUCTION SPACE FOR ESTIMATING CORRELATION DIMENSION

1996 ◽  
Vol 06 (02) ◽  
pp. 377-381 ◽  
Author(s):  
ROBERT C. HILBORN ◽  
MINGZHOU DING
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Correlation Dimension ◽  
Chaotic Time Series ◽  
Largest Lyapunov Exponent ◽  
Correlation Integral ◽  
Past Work ◽  
Optimal Reconstruction ◽  
Scaling Region ◽  
Delay Coordinates

In this paper we consider the estimation of the correlation dimension from a scalar chaotic time series using delay coordinates. Past work has shown that there appears to be a reconstruction space for which the correlation integral has the longest scaling region. We give a firmer foundation to this idea by developing a theory that estimates the dimension of this “optimal” reconstruction space in terms of dynamical quantities such as the largest Lyapunov exponent.

Correction of the Correlation Dimension for Noisy Time Series

1997 ◽  
Vol 07 (06) ◽  
pp. 1283-1294 ◽  
Author(s):  
D. Kugiumtzis
Keyword(s):  
Time Series ◽  
Noise Level ◽  
Correlation Dimension ◽  
Epileptic Seizures ◽  
Chaotic Time Series ◽  
Simple Method ◽  
Correlation Integral ◽  
Free Data ◽  
Correction Scheme ◽  
Eeg Data

In the computation of the correlation dimension of chaotic time series corrupted with observational noise, the scaling region is often masked resulting in deteriorated estimates. Here a simple method is proposed to correct the corrupted correlation integral based on the statistical properties of the Euclidean norm used to compute the noisy point interdistances. When the noise level is known, the corrected slope from the noisy data is very close to the slope for the noise-free data. Thus if the scaling property of the noise-free attractor holds for distances around the noise amplitude then the correct dimension can be inferred. The problem of estimating the correct noise level is discussed and a simple approach is proposed. Simulations with synthetic noisy chaotic time series demonstrate the efficiency of the correction scheme. Furthermore, the correction scheme is used to enhance correlation dimension estimates for the Taylor–Couette chaotic data and for EEG data from epileptic seizures.

Estimating correlation dimension from a chaotic time series: when does plateau onset occur?

1993 ◽  
Vol 69 (3-4) ◽  
pp. 404-424 ◽  
Author(s):  
Mingzhou Ding ◽  
Celso Grebogi ◽  
Edward Ott ◽  
Tim Sauer ◽  
James A. Yorke
Keyword(s):  
Time Series ◽  
Correlation Dimension ◽  
Chaotic Time Series

scholarly journals ESTIMATING CORRELATION DIMENSION IN CHAOTIC TIME SERIES

10.5109/13504 ◽  
2001 ◽  
Vol 33 (1/2) ◽  
pp. 63-71 ◽  
Author(s):  
Atsushi Kawaguchi ◽  
Takashi Yanagawa
Keyword(s):  
Time Series ◽  
Correlation Dimension ◽  
Chaotic Time Series

NOISE LEVEL ESTIMATION FOR A CHAOTIC TIME SERIES

2012 ◽  
Vol 22 (03) ◽  
pp. 1250052 ◽  
Author(s):  
PENGCHENG XU ◽  
W. K. LI ◽  
A. W. JAYAWARDENA
Keyword(s):  
Time Series ◽  
Noise Level ◽  
Correlation Dimension ◽  
Chaotic Time Series ◽  
Estimation Methods ◽  
Supremum Norm ◽  
Linear Estimation ◽  
Governing Equations ◽  
Correlation Integral ◽  
Noise Level Estimation

In this study, the correlation sum and the correlation integral for chaotic time series using the Supremum norm and the Euclidean norm are discussed. The correlation integrals are then used to develop governing equations for the correlation sum, noise level and correlation dimension in which the correlation dimension and the noise level are linearly dependent on each other. Some linear estimation methods for the noise level are then introduced by using these equations. The estimation methods are applied to four chaotic time series (two artificial and two real-world). By comparing the performances of the estimations of the noise level, the best estimating method is then suggested.

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