Topological analysis of chaotic time series data from the Belousov-Zhabotinskii reaction
SummaryWe have applied topological methods to analyze chaotic time series data from the Belousov-Zhabotinskii reaction. First, the periodic orbits shadowed by the data set were identified. Next, a three-dimensional embedding without self-intersections was constructed from the data set. The topological structure of that flow was visualized by constructing a branched manifold such that every periodic orbit in the flow could be held by the branched manifold. The branched manifold, or induced template, was computed using the three lowest-period orbits. The organization of the higher-period orbits predicted by this induced template was compared with the organization of the orbits reconstructed from the data set with excellent results. The consequences of the presence of certain knots found in the data are discussed.
Flood prediction using Time Series Data Mining
Summary This paper describes a novel approach to river flood prediction using Time Series Data Mining which combines chaos theory and data mining to characterize and predict events in complex, nonperiodic and chaotic time series. Geophysical phenomena, including earthquakes, floods and rainfall, represent a class of nonlinear systems termed chaotic, in which the relationships between variables in a system are dynamic and disproportionate, however completely deterministic. Chaos theory provides a structured explanation for irregular behavior and anomalies in systems that are not inherently stochastic. While nonlinear approaches such as Artificial Neural Networks, Hidden Markov Models and Nonlinear Prediction are useful in forecasting of daily discharge values in a river, the focus of these approaches is on forecasting magnitudes of future discharge values rather than the prediction of floods. The described Time Series Data Mining methodology focuses on the prediction of events where floods constitute the events in a river daily discharge time series. The methodology is demonstrated using data collected at the St. Louis gauging station located on the Mississippi River in the USA. Results associated with the impact of earliness of prediction and the acceptable risk-level vs. prediction accuracy are presented.
Time Series Prediction Using Lyapunov Exponents In Embedding Phase Space
This paper describes a novel method of chaotic time series prediction, which is based on the fundamental characteristic of chaotic behavior that sensitive dependence upon initial conditions (SDUIC), and Lyapunov exponents (LEs) is a measure of the SDUIC in chaotic systems. Because LEs of chaotic time series data provide a quantitative analysis of system dynamics in different embedding dimension after embedding a chaotic time series in different embedding dimension phase spaces, a novel multi-dimension chaotic time series prediction method using LEs is proposed in this paper. This is done by first reconstructing a phase space using chaotic time series, then using LEs as a quantitative parameter to predict an unknown phase space point, after transferring the phase space point to time domain, the predicted chaotic time series data can be obtained. The computer simulation result of simulation showed that the proposed method is simple, practical and effective.
neural network sensor network machine learning artificial neural network support vector machine deep learning time series data mining support vector vector machine wavelet transform data analysi deep neural network neural network model hidden markov model regression model deep neural anomaly detection gene expression data base generative adversarial network generative adversarial time series datum adversarial network experimental datum fourier series nearest neighbor support vector regression time series analysi missing datum data based moving average gene expression datum time series model series analysi lyapunov exponent series datum outlier detection dynamic time warping time series forecasting data mining algorithm panel datum time series prediction series model multivariate time series finite time unit root dynamic time linear and nonlinear series forecasting time warping distance measure financial time series series prediction integrated moving average experimental comparison multivariate time financial time dependent variable chaotic time series nonlinear time vegetation index nonlinear time series arima model fuzzy time large time anomaly detection method fuzzy time series chaotic time autoregressive integrated moving time series based air pollutant time series classification representation method fokker-planck equation series representation similarity analysi series classification univariate time series time series clustering unsupervised anomaly detection periodic pattern nearest neighbor classification time series dataset series data mining time series regression anomaly detection approach time series database series clustering observed time series forecasting time series local similarity long time series time series similarity series database fmri time series complex time indian stock market time series representation symbolic aggregate approximation complex time series forecasting time series data set series similarity fmri time time series anomaly large time series series data analysi series anomaly detection analyzing time series expression time series interrupted time series ucr time series time correction modeling time series clustering time series mining time series interrupted time series data based fourier series representation simple exponential smoothing early classification forecast time series time series subsequence sensor networks pose distributed index piecewise constant approximation quality time series mining time microarray time series incomplete time series massive time series large-scale time series analysing time series microarray time neural time series mri time neural time series data generated time series experiment visualizing time series called time series data set