Online chaotic time series prediction using unbiased composite kernel machine via Cholesky factorization

Support vector regression for approximating nonlinear dynamic systems is more delicate than the approximation of indicator functions in support vector classification, particularly for systems that involve multitudes of time scales in their sampled data. The kernel used for support vector learning determines the class of functions from which a support vector machine can draw its solution, and the choice of kernel significantly influences the performance of a support vector machine. In this paper, to bridge the gap between wavelet multiresolution analysis and kernel learning, the closed-form orthogonal wavelet is exploited to construct new multiscale asymmetric orthogonal wavelet kernels for linear programming support vector learning. The closed-form multiscale orthogonal wavelet kernel provides a systematic framework to implement multiscale kernel learning via dyadic dilations and also enables us to represent complex nonlinear dynamics effectively. To demonstrate the superiority of the proposed multiscale wavelet kernel in identifying complex nonlinear dynamic systems, two case studies are presented that aim at building parallel models on benchmark datasets. The development of parallel models that address the long-term/mid-term prediction issue is more intricate and challenging than the identification of series-parallel models where only one-step ahead prediction is required. Simulation results illustrate the effectiveness of the proposed multiscale kernel learning.

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“…The kernel (20) can be easily generalized to the multidimensional version by using the tensor product…”

Section: Construction Of the Multiscale Orthogonalmentioning

confidence: 99%

Multiscale Asymmetric Orthogonal Wavelet Kernel for Linear Programming Support Vector Learning and Nonlinear Dynamic Systems Identification

Sun

Butts

2014

IEEE Trans. Cybern.

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“…Recently, researchers found that the prediction precision can be improved by using some combined techniques. These include artificial neural networks combined with fuzzy theory [9,10], the unbiased composite kernel LSSVR [11], and -nearest neighbors with phase space reconstruction [12]. Generally, these methods can obtain better results than traditional individual models, but they are complex, and the parameter selection is affected by personal experience.…”

Section: Introductionmentioning

confidence: 99%

The Adaptive-Clustering and Error-Correction Method for Forecasting Cyanobacteria Blooms in Lakes and Reservoirs

Bai¹,

Zhang²,

Wang³

et al. 2017

Advances in Mathematical Physics

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Globally, cyanobacteria blooms frequently occur, and effective prediction of cyanobacteria blooms in lakes and reservoirs could constitute an essential proactive strategy for water-resource protection. However, cyanobacteria blooms are very complicated because of the internal stochastic nature of the system evolution and the external uncertainty of the observation data. In this study, an adaptive-clustering algorithm is introduced to obtain some typical operating intervals. In addition, the number of nearest neighbors used for modeling was optimized by particle swarm optimization. Finally, a fuzzy linear regression method based on error-correction was used to revise the model dynamically near the operating point. We found that the combined method can characterize the evolutionary track of cyanobacteria blooms in lakes and reservoirs. The model constructed in this paper is compared to other cyanobacteria-bloom forecasting methods (e.g., phase space reconstruction and traditional-clustering linear regression), and, then, the average relative error and average absolute error are used to compare the accuracies of these models. The results suggest that the proposed model is superior. As such, the newly developed approach achieves more precise predictions, which can be used to prevent the further deterioration of the water environment.

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SAR Image Fast Online ATR Based on Visual Attention and Scale Analysis

Wang

Cai

Yao

et al. 2019

Communications in Computer and Information Science

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Online chaotic time series prediction using unbiased composite kernel machine via Cholesky factorization

Cited by 12 publications

References 29 publications

Multiscale Asymmetric Orthogonal Wavelet Kernel for Linear Programming Support Vector Learning and Nonlinear Dynamic Systems Identification

Multiscale Asymmetric Orthogonal Wavelet Kernel for Linear Programming Support Vector Learning and Nonlinear Dynamic Systems Identification

The Adaptive-Clustering and Error-Correction Method for Forecasting Cyanobacteria Blooms in Lakes and Reservoirs

SAR Image Fast Online ATR Based on Visual Attention and Scale Analysis

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