Multi-variable regression methods using modified Chebyshev polynomials of class 2

Li, Zibo; Sun, Guangmin; He, Cunfu; Liu, Xiucheng; Zhang, Ruihuan; Liu, Yu; Zhao, Dequn; Líu, Hao; Zhang, Fan

doi:10.1016/j.cam.2018.04.022

Cited by 5 publications

(14 citation statements)

References 20 publications

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“…0.3629) is achieved by MIFS-CR+CP-2. This high performance could be ascribed to three aspects: Firstly, given a proper order, any nonlinear model could be approximated by an orthogonal polynomials; Secondly, compared with the NN-based model, a specific mathematical equation could be deducted by the polynomials-based model; Thirdly, according to the theory of PCPR, the basic idea of PCPR is to enhance the efficiency with the cost of accuracy [12] and therefore the prediction error is slightly larger than feature-selection-based MCPR method (i.e. MIFS-CR+CP-2).…”

Section: Resultsmentioning

confidence: 99%

“…However, the number of regressed coefficients of MCPR is exponentially proportion to the number of input variables. To overcome the coefficient explosion problem, in our work [12] , two strategies including feature selection and cascaded regression are designed to alleviate this problem. In terms of feature selection idea, a novel feature selection method [13] named "Mutual Information-based Feature Selection with Class-dependent Redundancy" (MIFS-CR) are combined with MCPR to directly reduce the number of the input variables of MCPR.…”

Section: Introduction To Regression Methodsmentioning

confidence: 99%

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Prediction of the Hardness of X12m Using Barkhausen Noise and Chebyshev Polynomials Regression Methods

Li²,

Wang³

et al. 2020

Studies in Applied Electromagnetics and Mechanics

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Barkhausen noise (BN) is electromagnetic pulse sequence that could be used to nondestructively predict the properties of materials such as hardness, residual stress and carbon content. Current BN signal analysis methods fail to describe the highly variated BN signal and achieve high regression accuracy due to the low interpretability of neural network and limited capacity of mathematical regression tools. In this paper, two multi-variable regression tools, named partial Chebyshev polynomial regression (PCPR) and Mutual Information-based Feature Selection with Class-dependent Redundancy and multi-variable Chebyshev polynomials regression (MIFS-CR+MCPR), are employed for the first time to predict the hardness of Cr12MoV steel (i.e. X12m). Combined with Chebyshev polynomials, our regression tools are designed on the basis of cascaded regression and mutual-information-based feature selection. As represented by the experimental results for predicting the hardness of X12m, the proposed method outperforms other comparative methods including neural network and partial linear square regression method.

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Section: Resultsmentioning

confidence: 99%

Section: Introduction To Regression Methodsmentioning

confidence: 99%

Prediction of the Hardness of X12m Using Barkhausen Noise and Chebyshev Polynomials Regression Methods

Li²,

Wang³

et al. 2020

Studies in Applied Electromagnetics and Mechanics

Self Cite

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“…The limitation of our regression methods is draw as:The manifold optimization might not be stable in the case of multi-variable function exploitation.The proposed regression methods mentioned in this paper are not suitable for the classification problem.The kernel trick employed in recent regression studies could not be used in the proposed regression methods. Based on the research (Li et al. , 2019), we had tried to apply the kernel trick to PCPR by using the idea of K-PLSR (Rosipal and Trejo, 2001).…”

Section: Discussionmentioning

confidence: 99%

“…, 2014; Zhou et al. , 2015) was adopted to simplify a multi-variable regression problem by using the combination of several single (or bi-, tri-) variable regression problems instead of a unified multi-variable problem (more specific information in (Li et al. , 2019)).…”

Section: Introductionmentioning

confidence: 99%

Comparative study for multi-variable regression methods based on Laguerre polynomial and manifolds optimization

Yan

Li³

et al. 2022

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PurposeThe purpose of this paper is to overcome the application limitations of other multi-variable regression based on polynomials due to the huge computation room and time cost.Design/methodology/approachIn this paper, based on the idea of feature selection and cascaded regression, two strategies including Laguerre polynomials and manifolds optimization are proposed to enhance the accuracy of multi-variable regression. Laguerre polynomials were combined with the genetic algorithm to enhance the capacity of polynomials approximation and the manifolds optimization method was introduced to solve the co-related optimization problem.FindingsTwo multi-variable Laguerre polynomials regression methods are designed. Firstly, Laguerre polynomials are combined with feature selection method. Secondly, manifolds component analysis is adopted in cascaded Laguerre polynomials regression method. Two methods are brought to enhance the accuracy of multi-variable regression method.Research limitations/implicationsWith the increasing number of variables in regression problem, the stable accuracy performance might not be kept by using manifold-based optimization method. Moreover, the methods mentioned in this paper are not suitable for the classification problem.Originality/valueExperiments are conducted on three types of datasets to evaluate the performance of the proposed regression methods. The best accuracy was achieved by the combination of cascade, manifold optimization and Chebyshev polynomials, which implies that the manifolds optimization has stronger contribution than the genetic algorithm and Laguerre polynomials.

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“…Chebyshev polynomials have become very important in numerical analysis. They are widely used because of their advantages, such as the roots of the first kind of Chebyshev polynomials (Gauss-Lobatto nodes) being used in polynomial interpolation for minimizing the Runge phenomena, providing the best uniform approximation of polynomials in continuous functions (see [35][36][37]). Most commonly used techniques with Chebyshev polynomials have been examined in [38][39][40] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Modified Chebyshev collocation method for delayed predator–prey system

Dengata

2020

Adv Differ Equ

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In this study, the approximate solutions of the predator-prey system with delay have been obtained by using the modified Chebyshev collocation method. The main technique is that this method transforms the original problem into a system of nonlinear algebraic equations. By using the residual function of the operator equations, error differential equations are constructed and thus the approximate solutions are corrected. A numerical example is given to confirm the reliability and applicability of the method, and comparisons with existing results are given. The numerical results show that the obtained solutions are in good agreement with earlier studies.

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Multi-variable regression methods using modified Chebyshev polynomials of class 2

Cited by 5 publications

References 20 publications

Prediction of the Hardness of X12m Using Barkhausen Noise and Chebyshev Polynomials Regression Methods

Prediction of the Hardness of X12m Using Barkhausen Noise and Chebyshev Polynomials Regression Methods

Comparative study for multi-variable regression methods based on Laguerre polynomial and manifolds optimization

Modified Chebyshev collocation method for delayed predator–prey system

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