A projection wavelet weighted twin support vector regression and its primal solution

Wang, Lidong; Gao, Chuang; Zhao, Nannan; Chen, Xuebo

doi:10.1007/s10489-019-01422-7

Cited by 14 publications

(5 citation statements)

References 21 publications

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“…According to Ref. [19], the first-order and second-order gradients of L 1 for u 1 and L 2 for u 2 is expressed as follows…”

Section: The Regression Function Is As Followsmentioning

confidence: 99%

“…At present, there are many kinds of kernel functions, and choosing a suitable kernel function has a great influence on the performance of the algorithm. Wang et al [ 19 ] studied the performance of six kernel functions, including linear kernel function, polynomial kernel function, Sigmoid kernel function, multiquadric kernel function, log kernel function, and Gaussian kernel function. Finally, it proved that Gaussian kernel function has better performance.…”

Section: Establishment Of Mathematical Model For Dynamic Control Of 2...mentioning

confidence: 99%

“…According to Ref. [19], the first‐order and second‐order gradients of L 1 for u 1 and L 2 for u 2 is expressed as follows

\begin{matrix} \nabla L_{1} (u_{1}) = Q_{1} u_{1} - P_{1} + c_{3} G^{normalT} D diag (\frac{1}{1 + \exp (- α (G u_{1} - f_{1}))}) \\ \nabla^{2} L_{1} (u_{1}) = Q_{1} + α c_{3} G^{normalT} D diag (\frac{exp (- α (G u_{1} - f_{1}))}{1 + exp {(- α (G u_{1} - f_{1}))}^{2}}) G \end{matrix}

\begin{matrix} \nabla L_{2} (u_{2}) = Q_{2} u_{2} ‐ P_{2} + c_{6} G^{normalT} D diag (\frac{1}{1 + exp (- α (f_{2} - G u_{2}))}) \\ \nabla^{2} L_{2} (u_{2}) = Q_{2} + α c_{6} G^{normalT} D diag (\frac{exp (- α (f_{2} - G u_{2}))}{1 + exp {(- α (f_{2} - G u_{2}))}^{2}}) ... \end{matrix}

…”

Section: Establishment Of Mathematical Model For Dynamic Control Of 2...mentioning

confidence: 99%

“…Gupta [ 18 ] proposed an unconstrained problems K‐nearest neighbor weight twin support vector regression (KNNUPWTSVR), which solved the objective function in the original solution space and improved the operation speed. In 2019, Wang et al [ 19 ] proposed projection wavelet weighted twin support vector regression (PWWTSVR), which reduced the effect of noise in training samples by introducing wavelet transform and finding a projection axis in each objective function to minimize the variance of projected points. Compared with the aforementioned improved TSVR, the PWWTSVR algorithm had better generalization ability and higher computational efficiency.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

End‐Point Dynamic Control Model for 260 Tons BOF Steelmaking Based on PWWTSVR and LWOA

Wang

Gao

et al. 2023

steel research int.

Self Cite

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The end-point carbon content and temperature are two important factors that affect steel quality in the basic oxygen furnace (BOF) production process. [1] The BOF end-point control [2] can affect the quality of subsequent products and production costs of expenditure. Therefore, the research on BOF end-point control is particularly important. At present, some mathematical models can be established to realize the control of the BOF end-point, which are the static control model and dynamic control model. The static control model is based on the initial smelting conditions, using mechanisms, [3] statistics, [4] and other algorithms to establish a model for related calculations. Due to the changes in the blowing process that cannot be monitored and adjusted in time, and the accuracy cannot be improved. The dynamic control model is based on the static control model, which is mainly to dynamically monitor the blowing process in the later stage of smelting to adjust the parameters. Compared with the static control model, the dynamic control model has higher accuracy. Therefore, it is very meaningful to deeply investigate the dynamic control model. The premise of establishing a dynamic control model is based on an accurate prediction model, and the results of the prediction model can affect the proposed control model. Therefore, it is necessary to establish an accurate BOF end-point prediction model. With the application development of artificial intelligence technology and computer network technology, the neural network has been applied to BOF end-point prediction by many scholars. [5][6][7][8][9][10] Cox et al. [5] established a converter end-point prediction model based on the artificial neural network, which was used to predict the oxygen blowing volume and coolant addition at the end of the blowing period. Jim'enez et al. [6] used an artificial neural network to establish a prediction model to predict the temperature of molten iron. Fileti et al. [7] established an inverse neural model to adjust the oxygen and coolant required for the end-blow stage. Wang et al. [8] proposed a prediction model based on the combination of a genetic algorithm and back propagation (BP) neural network and verified that the combined model has a high end-point hit rate (HR). Wang et al. [9] combined a weighted clustering algorithm with a polynomial neural network to establish a converter end-point prediction model, which could effectively predict the end-point phosphorus content of molten steel. He et al. [10] used principal component analysis to reduce the dimension of the input variables of the prediction model, and then used BP neural network to establish a prediction model for the end-point phosphorus content of the converter. The previous research has achieved good results. However, the neural network may fall into the local optimal problem when establishing the prediction model, which could not improve the accuracy of the model. Support vector regression (SVR) is an intelligent algorithm for regression problems proposed by Cortes et ...

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“…According to Ref. [19], the first-order and second-order gradients of L 1 for u 1 and L 2 for u 2 is expressed as follows…”

Section: The Regression Function Is As Followsmentioning

confidence: 99%

Section: Establishment Of Mathematical Model For Dynamic Control Of 2...mentioning

confidence: 99%

“…According to Ref. [19], the first‐order and second‐order gradients of L 1 for u 1 and L 2 for u 2 is expressed as follows

\begin{matrix} \nabla L_{1} (u_{1}) = Q_{1} u_{1} - P_{1} + c_{3} G^{normalT} D diag (\frac{1}{1 + \exp (- α (G u_{1} - f_{1}))}) \\ \nabla^{2} L_{1} (u_{1}) = Q_{1} + α c_{3} G^{normalT} D diag (\frac{exp (- α (G u_{1} - f_{1}))}{1 + exp {(- α (G u_{1} - f_{1}))}^{2}}) G \end{matrix}

\begin{matrix} \nabla L_{2} (u_{2}) = Q_{2} u_{2} ‐ P_{2} + c_{6} G^{normalT} D diag (\frac{1}{1 + exp (- α (f_{2} - G u_{2}))}) \\ \nabla^{2} L_{2} (u_{2}) = Q_{2} + α c_{6} G^{normalT} D diag (\frac{exp (- α (f_{2} - G u_{2}))}{1 + exp {(- α (f_{2} - G u_{2}))}^{2}}) ... \end{matrix}

…”

Section: Establishment Of Mathematical Model For Dynamic Control Of 2...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

End‐Point Dynamic Control Model for 260 Tons BOF Steelmaking Based on PWWTSVR and LWOA

Wang

Gao

et al. 2023

steel research int.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Gu et al [24] also have investigated a new fast clustering-based approach for TSVR to lessen the effect of outliers and noise in the observed data examples by following the prior structural information and successive over relaxation algorithm. Due to influence of noise and outliers in observed real world data, SVR and TSVR regression based models attract in the literature [49,51,77,81]; Wang et al [66][67][68].…”

Section: Introductionmentioning

confidence: 99%

On Regularization Based Twin Support Vector Regression with Huber Loss

Gupta

2021

Neural Process Lett

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Twin support vector regression (TSVR) is generally employed with ε-insensitive loss function which is not well capable to handle the noises and outliers. According to the definition, Huber loss function performs as quadratic for small errors and linear for others and shows better performance in comparison to Gaussian loss hence it restrains easily for a different type of noises and outliers. Recently, TSVR with Huber loss (HN-TSVR) has been suggested to handle the noise and outliers. Like TSVR, it is also having the singularity problem which degrades the performance of the model. In this paper, regularized version of HN-TSVR is proposed as regularization based twin support vector regression (RHN-TSVR) to avoid the singularity problem of HN-TSVR by applying the structured risk minimization principle that leads to our model convex and well-posed. This proposed RHN-TSVR model is well capable to handle the noise as well as outliers and avoids the singularity issue. To show the validity and applicability of proposed RHN-TSVR, various experiments perform on several artificial generated datasets having uniform, Gaussian and Laplacian noise as well as on benchmark different real-world datasets and compare with support vector regression, TSVR, ε-asymmetric Huber SVR, ε-support vector quantile regression and HN-TSVR. Here, all benchmark real-world datasets are embedded with a different significant level of noise 0%, 5% and 10% on different reported algorithms with the proposed approach. The proposed algorithm RHN-TSVR is showing better prediction ability on artificial datasets as well as real-world datasets with a different significant level of noise compared to other reported models.

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Fast clustering-based weighted twin support vector regression

Fang

Pan

et al. 2020

Soft Comput

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A projection wavelet weighted twin support vector regression and its primal solution

Cited by 14 publications

References 21 publications

End‐Point Dynamic Control Model for 260 Tons BOF Steelmaking Based on PWWTSVR and LWOA

End‐Point Dynamic Control Model for 260 Tons BOF Steelmaking Based on PWWTSVR and LWOA

On Regularization Based Twin Support Vector Regression with Huber Loss

Fast clustering-based weighted twin support vector regression

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