Phase Space Reconstruction

"Data-driven techniques such as Auto-Regressive Moving Average (ARMA), K-Nearest-Neighbors (KNN), and Artificial Neural Networks (ANN), are widely applied to hydrologic time series prediction. This paper investigates different data-driven models to determine the optimal approach of predicting monthly streamflow time series. Four sets of data from different locations of People’s Republic of China (Xiangjiaba, Cuntan, Manwan, and Danjiangkou) are applied for the investigation process. Correlation integral and False Nearest Neighbors (FNN) are first employed for Phase Space Reconstruction (PSR). Four models, ARMA, ANN, KNN, and Phase Space Reconstruction-based Artificial Neural Networks (ANN-PSR) are then compared by one-month-ahead forecast using Cuntan and Danjiangkou data. The KNN model performs the best among the four models, but only exhibits weak superiority to ARMA. Further analysis demonstrates that a low correlation between model inputs and outputs could be the main reason to restrict the power of ANN. A Moving Average Artificial Neural Networks (MA-ANN), using the moving average of streamflow series as inputs, is also proposed in this study. The results show that the MA-ANN has a significant improvement on the forecast accuracy compared with the original four models. This is mainly due to the improvement of correlation between inputs and outputs depending on the moving average operation. The optimal memory lengths of the moving average were three and six for Cuntan and Danjiangkou respectively when the optimal model inputs are recognized as the previous twelve months.

Keywords: Hydrologic time series; Auto regressive moving average; K nearest neighbors; Artificial neural networks; Phase space reconstruction; False nearest neighbors; Dynamics of chaos"

Many methods for automatic heartbeat classification have been applied and reported in literature, but relatively few of them concerned with patient independent classification because of the less significant results compared to patient dependent ones. In this work, using phase space reconstruction in order to classify five heartbeat types can fill this gap to some extent. In the first and second method, Reconstructed phase space (RPS) is modeled by the Gaussian mixture model (GMM) and bins, respectively, and then classified by classic Bayesian classifier. In the third method, RPS is directly used to train predictor time-delayed neural networks (TDNN) and classified based on minimum prediction error. All three methods highly outperform the results reported before, for patient independent heartbeat classification. The best result is achieved using GMM–Bayes method with 92.5% classification accuracy.

In phase space reconstruction of time series, the selection of embedding dimension is important. Based on the idea of checking the behavior of near neighbors in the reconstruction dimension, a new method to determine proper minimum embedding dimension is constructed. This method has a sound theoretical basis and can lead to good result. It can indicate the noise level in the data to be reconstructed, and estimate the reconstruction quality. It is applied to speech signal reconstruction and the generic embedding dimension of speech signals is deduced.

Traffic congestions problem could affect everyday life especially in urban area. In order to solve the issue, an excellent traffic flow prediction needs to be developed for a better traffic management. Hence, this study was conducted in order to predict traffic flow by using the data of total volume of vehicles per hour at two main roads located in urban areas namely Selangor and Kuala Lumpur, Malaysia by using application of chaos theory. Phase space reconstruction was used to determine the chaotic behaviour of the total volume of vehicles per hour data. The reconstruction of phase space involves a single variable of the total volume of vehicles per hour data to m-dimensional phase space. Meanwhile, the inverse approach as well as local linear approximation method was used to develop prediction model of the traffic flow time series data. This study found that (i) the time series data were chaotic behaviour based on the phase space plot and (ii) inverse approach can provide predicti...

The use of phase-space reconstruction approach for understanding and predicting suspended sediment concentration dynamics in rivers is investigated. According to this approach, the dynamic changes of the suspended sediment concentration phenomenon are represented by reconstructing (or embedding) the single-dimensional (or variable) suspended sediment concentration series in a multi-dimensional phase-space. After representing the dynamics in the phase-space, a local approximation method is employed for making predictions. The approach is employed for representing and predicting the dynamics of the daily suspended sediment concentration observed in the Mississippi River basin (at St. Louis, MO) in the United States of America. The predicted suspended sediment concentrations are found to be in very good agreement with the observed ones; not only are the major trends well captured but the minor (noisy) ¯uctuations reasonably preserved as well. The near-accurate predictions indicate the ...

Summary Forecasting activities are widely performed in the various areas of supply chains for predicting important supply chain management(SCM) measurements such as demand volume in order management, product quality in manufacturing processes, capacity usage in production management, traffic costs in transportation management, and so on. The accuracy of forecasting has a great influence on the efficiency of SCM. According to

Time delays phase space reconstruction represents one of useful tools of nonlinear time series analysis, enabling number of applications. Its utilization requires the value of time delay to be known, as well as the value of embedding dimension. There are sev- eral methods how to estimate both these parameters. Typically, time delay is computed first, followed by embedding dimension. Our