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In the paper, a novel kernel recursive least-squares (KRLS) algorithm named random Fourier feature kernel recursive maximum mixture correntropy (RFF-RMMC) algorithm is proposed, which improves the prediction efficiency and robustness of the KRLS algorithm. Random Fourier feature (RFF) method as well as maximum mixture correntropy criterion (MMCC) are combined and applied into KRLS algorithm afterwards. Using RFF to approximate the kernel function in KRLS with a fixed cost can greatly reduce the computational complexity and simultaneously improve the prediction efficiency. In addition, the MMCC maintains the robustness like the maximum correntropy criterion (MCC). More importantly, it can enhance the accuracy of the similarity measurement between predicted and true values by more flexible parameter settings, and then make up for the loss of prediction accuracy caused by RFF to a certain extent. The performance of the RFF-RMMC algorithm for online time series prediction is verified by the simulation results based on three datasets.
Xinghan Xu; Weijie Ren. Random Fourier feature kernel recursive maximum mixture correntropy algorithm for online time series prediction. ISA Transactions 2021, 1 .
AMA StyleXinghan Xu, Weijie Ren. Random Fourier feature kernel recursive maximum mixture correntropy algorithm for online time series prediction. ISA Transactions. 2021; ():1.
Chicago/Turabian StyleXinghan Xu; Weijie Ren. 2021. "Random Fourier feature kernel recursive maximum mixture correntropy algorithm for online time series prediction." ISA Transactions , no. : 1.
Predicting for long-term dynamics of complex systems from observations is a challenging topic in the field of time series modeling and analysis, and is continually under research. Noteworthily, multi-step prediction requires accurate learning of dynamics and correlations between historical data for predicting future behavior. In this paper, we proposed a modified recurrent neural network named hierarchical delay-memory echo state network (HDESN) for solving the task of multi-step chaotic time series prediction. The HDESN uses multiple reservoirs with delay-memory capabilities, which can simultaneously discover and explore the information of short-term and long-term memory hidden in the historical sequence, and extract the valuable evolution patterns through deep topology and hierarchical processing. Moreover, to ensure high-quality prediction results and reduce the computational burden as much as possible, we further design a phase-space representation strategy which can calculate a compact topology and delay-memory coefficient according to the chaotic characteristics of the data. Compared with other improved ESN-based models, the proposed HDESN does not have a larger memory capacity to capture potential evolution law hidden in the complex system layer by layer, but can also adaptively determine a suitable network architecture to reflect the mapping relations in chaotic phase space. The experimental results on two benchmark chaotic systems and a real-world meteorological dataset demonstrate that the proposed HDESN model obtains satisfactory performance in multi-step chaotic time series prediction.
Xiaodong Na; Weijie Ren; Xinghan Xu. Hierarchical delay-memory echo state network: A model designed for multi-step chaotic time series prediction. Engineering Applications of Artificial Intelligence 2021, 102, 104229 .
AMA StyleXiaodong Na, Weijie Ren, Xinghan Xu. Hierarchical delay-memory echo state network: A model designed for multi-step chaotic time series prediction. Engineering Applications of Artificial Intelligence. 2021; 102 ():104229.
Chicago/Turabian StyleXiaodong Na; Weijie Ren; Xinghan Xu. 2021. "Hierarchical delay-memory echo state network: A model designed for multi-step chaotic time series prediction." Engineering Applications of Artificial Intelligence 102, no. : 104229.
With the acceleration of urbanization, there is an increasing trend of heavy pollution. PM2.5, also known as fine particulate matter, refers to particles in the atmosphere with a diameter of less than or equal to 2.5 microns. PM2.5 has a serious impact on human life, a sustainable city, national economic development, and so on. How to forecast the PM2.5 concentration accurately, and then formulate a scientific air pollution prevention and monitoring program is of great significance. This paper proposes a hybrid model based on echo state network (ESN) and an improved particle swarm optimization (IPSO) algorithm for the Beijing air pollution problem, and provides a method for PM2.5 concentration forecasting. Firstly, the PSO algorithm is improved to speed up the search performance. Secondly, the optimal subset of the original data is selected by the convergence cross-mapping (CCM) method. Thirdly, the phase space reconstruction (PSR) process is combined with the forecasting model, and some parameters are optimized by the IPSO. Finally, the optimal variable subset is used to predict PM2.5 concentration. The 11-dimensional air quality data in Beijing from January 1 to December 31, 2016 are analyzed by the proposed method. The experimental results show that the hybrid method is superior to other comparative models in several evaluation indicators, both in one-step and multi-step forecasting of PM2.5 time series. The hybrid model has good application prospects in air quality forecasting and monitoring.
Xinghan Xu; Weijie Ren. Application of a Hybrid Model Based on Echo State Network and Improved Particle Swarm Optimization in PM2.5 Concentration Forecasting: A Case Study of Beijing, China. Sustainability 2019, 11, 3096 .
AMA StyleXinghan Xu, Weijie Ren. Application of a Hybrid Model Based on Echo State Network and Improved Particle Swarm Optimization in PM2.5 Concentration Forecasting: A Case Study of Beijing, China. Sustainability. 2019; 11 (11):3096.
Chicago/Turabian StyleXinghan Xu; Weijie Ren. 2019. "Application of a Hybrid Model Based on Echo State Network and Improved Particle Swarm Optimization in PM2.5 Concentration Forecasting: A Case Study of Beijing, China." Sustainability 11, no. 11: 3096.
The prediction of chaotic time series has been a popular research field in recent years. Due to the strong non-stationary and high complexity of the chaotic time series, it is difficult to directly analyze and predict depending on a single model, so the hybrid prediction model has become a promising and favorable alternative. In this paper, we put forward a novel hybrid model based on a two-layer decomposition approach and an optimized back propagation neural network (BPNN). The two-layer decomposition approach is proposed to obtain comprehensive information of the chaotic time series, which is composed of complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and variational mode decomposition (VMD). The VMD algorithm is used for further decomposition of the high frequency subsequences obtained by CEEMDAN, after which the prediction performance is significantly improved. We then use the BPNN optimized by a firefly algorithm (FA) for prediction. The experimental results indicate that the two-layer decomposition approach is superior to other competing approaches in terms of four evaluation indexes in one-step and multi-step ahead predictions. The proposed hybrid model has a good prospect in the prediction of chaotic time series.
Xinghan Xu; Weijie Ren; Xu; Ren. A Hybrid Model Based on a Two-Layer Decomposition Approach and an Optimized Neural Network for Chaotic Time Series Prediction. Symmetry 2019, 11, 610 .
AMA StyleXinghan Xu, Weijie Ren, Xu, Ren. A Hybrid Model Based on a Two-Layer Decomposition Approach and an Optimized Neural Network for Chaotic Time Series Prediction. Symmetry. 2019; 11 (5):610.
Chicago/Turabian StyleXinghan Xu; Weijie Ren; Xu; Ren. 2019. "A Hybrid Model Based on a Two-Layer Decomposition Approach and an Optimized Neural Network for Chaotic Time Series Prediction." Symmetry 11, no. 5: 610.
Air pollution has become a global environmental problem, because it has a great adverse impact on human health and the climate. One way to explore this problem is to monitor and predict air quality index in an economical way. Accurate monitoring and prediction of air quality index (AQI), e.g., PM2.5 concentration, is a challenging task. In order to accurately predict the PM2.5 time series, we propose a supplementary leaky integrator echo state network (SLI-ESN) in this paper. It adds the historical state term of the historical moment to the calculation of leaky integrator reservoir, which improves the influence of historical evolution state on the current state. Considering the redundancy and correlation between multivariable time series, minimum redundancy maximum relevance (mRMR) feature selection method is introduced to reduce redundant and irrelevant information, and increase computation speed. A variety of evaluation indicators are used to assess the overall performance of the proposed method. The effectiveness of the proposed model is verified by the experiment of Beijing PM2.5 time series prediction. The comparison of learning time also shows the efficiency of the algorithm.
Xinghan Xu; Weijie Ren. Prediction of Air Pollution Concentration Based on mRMR and Echo State Network. Applied Sciences 2019, 9, 1811 .
AMA StyleXinghan Xu, Weijie Ren. Prediction of Air Pollution Concentration Based on mRMR and Echo State Network. Applied Sciences. 2019; 9 (9):1811.
Chicago/Turabian StyleXinghan Xu; Weijie Ren. 2019. "Prediction of Air Pollution Concentration Based on mRMR and Echo State Network." Applied Sciences 9, no. 9: 1811.