Gradient/Hessian-enhanced least square support vector regression

In least square support vector regression (LSSVR), Vapnik's original SVR formulation has been modified by using a cost function which corresponds to a form of ridge regression rather than ε-insensitive loss function. As a result, nonlinear function estimation is done by solving linear set of eq...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Jiang, Ting [verfasserIn] Zhou, XiaoJian [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	Algorithms Least square support vector regression Metamodel Gradient Hessian

Übergeordnetes Werk:	Enthalten in: Information processing letters - Amsterdam [u.a.] : Elsevier, 1971, 134, Seite 1-8
Übergeordnetes Werk:	volume:134 ; pages:1-8

DOI / URN:	10.1016/j.ipl.2018.01.014

Katalog-ID:	ELV00147085X

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520			\|a In least square support vector regression (LSSVR), Vapnik's original SVR formulation has been modified by using a cost function which corresponds to a form of ridge regression rather than ε-insensitive loss function. As a result, nonlinear function estimation is done by solving linear set of equations instead of solving a time-consuming quadratic programming problem. When the gradient/Hessians in samples can be obtained cheaply, it should be considered in the construction of metamodels. In this paper, the gradient/Hessian-enhanced LSSVR (G/HELSSVR) is developed through incorporating gradient/Hessian information into the traditional LSSVR. The performance of this method is tested by analytical function fitting. The experimental results illustrate that the proposed G/HELSSVR model has a great advantages over the traditional LSSVR and gradient-enhanced LSSVR (GELSSVR).
650		4	\|a Algorithms
650		4	\|a Least square support vector regression
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650		4	\|a Hessian
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allfields	10.1016/j.ipl.2018.01.014 doi (DE-627)ELV00147085X (ELSEVIER)S0020-0190(18)30029-2 DE-627 ger DE-627 rda eng 004 DE-600 54.00 bkl Jiang, Ting verfasserin aut Gradient/Hessian-enhanced least square support vector regression 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In least square support vector regression (LSSVR), Vapnik's original SVR formulation has been modified by using a cost function which corresponds to a form of ridge regression rather than ε-insensitive loss function. As a result, nonlinear function estimation is done by solving linear set of equations instead of solving a time-consuming quadratic programming problem. When the gradient/Hessians in samples can be obtained cheaply, it should be considered in the construction of metamodels. In this paper, the gradient/Hessian-enhanced LSSVR (G/HELSSVR) is developed through incorporating gradient/Hessian information into the traditional LSSVR. The performance of this method is tested by analytical function fitting. The experimental results illustrate that the proposed G/HELSSVR model has a great advantages over the traditional LSSVR and gradient-enhanced LSSVR (GELSSVR). Algorithms Least square support vector regression Metamodel Gradient Hessian Zhou, XiaoJian verfasserin aut Enthalten in Information processing letters Amsterdam [u.a.] : Elsevier, 1971 134, Seite 1-8 Online-Ressource (DE-627)265783771 (DE-600)1466301-6 (DE-576)074890921 1872-6119 nnns volume:134 pages:1-8 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 54.00 Informatik: Allgemeines AR 134 1-8
spelling	10.1016/j.ipl.2018.01.014 doi (DE-627)ELV00147085X (ELSEVIER)S0020-0190(18)30029-2 DE-627 ger DE-627 rda eng 004 DE-600 54.00 bkl Jiang, Ting verfasserin aut Gradient/Hessian-enhanced least square support vector regression 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In least square support vector regression (LSSVR), Vapnik's original SVR formulation has been modified by using a cost function which corresponds to a form of ridge regression rather than ε-insensitive loss function. As a result, nonlinear function estimation is done by solving linear set of equations instead of solving a time-consuming quadratic programming problem. When the gradient/Hessians in samples can be obtained cheaply, it should be considered in the construction of metamodels. In this paper, the gradient/Hessian-enhanced LSSVR (G/HELSSVR) is developed through incorporating gradient/Hessian information into the traditional LSSVR. The performance of this method is tested by analytical function fitting. The experimental results illustrate that the proposed G/HELSSVR model has a great advantages over the traditional LSSVR and gradient-enhanced LSSVR (GELSSVR). Algorithms Least square support vector regression Metamodel Gradient Hessian Zhou, XiaoJian verfasserin aut Enthalten in Information processing letters Amsterdam [u.a.] : Elsevier, 1971 134, Seite 1-8 Online-Ressource (DE-627)265783771 (DE-600)1466301-6 (DE-576)074890921 1872-6119 nnns volume:134 pages:1-8 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 54.00 Informatik: Allgemeines AR 134 1-8
allfields_unstemmed	10.1016/j.ipl.2018.01.014 doi (DE-627)ELV00147085X (ELSEVIER)S0020-0190(18)30029-2 DE-627 ger DE-627 rda eng 004 DE-600 54.00 bkl Jiang, Ting verfasserin aut Gradient/Hessian-enhanced least square support vector regression 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In least square support vector regression (LSSVR), Vapnik's original SVR formulation has been modified by using a cost function which corresponds to a form of ridge regression rather than ε-insensitive loss function. As a result, nonlinear function estimation is done by solving linear set of equations instead of solving a time-consuming quadratic programming problem. When the gradient/Hessians in samples can be obtained cheaply, it should be considered in the construction of metamodels. In this paper, the gradient/Hessian-enhanced LSSVR (G/HELSSVR) is developed through incorporating gradient/Hessian information into the traditional LSSVR. The performance of this method is tested by analytical function fitting. The experimental results illustrate that the proposed G/HELSSVR model has a great advantages over the traditional LSSVR and gradient-enhanced LSSVR (GELSSVR). Algorithms Least square support vector regression Metamodel Gradient Hessian Zhou, XiaoJian verfasserin aut Enthalten in Information processing letters Amsterdam [u.a.] : Elsevier, 1971 134, Seite 1-8 Online-Ressource (DE-627)265783771 (DE-600)1466301-6 (DE-576)074890921 1872-6119 nnns volume:134 pages:1-8 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 54.00 Informatik: Allgemeines AR 134 1-8
allfieldsGer	10.1016/j.ipl.2018.01.014 doi (DE-627)ELV00147085X (ELSEVIER)S0020-0190(18)30029-2 DE-627 ger DE-627 rda eng 004 DE-600 54.00 bkl Jiang, Ting verfasserin aut Gradient/Hessian-enhanced least square support vector regression 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In least square support vector regression (LSSVR), Vapnik's original SVR formulation has been modified by using a cost function which corresponds to a form of ridge regression rather than ε-insensitive loss function. As a result, nonlinear function estimation is done by solving linear set of equations instead of solving a time-consuming quadratic programming problem. When the gradient/Hessians in samples can be obtained cheaply, it should be considered in the construction of metamodels. In this paper, the gradient/Hessian-enhanced LSSVR (G/HELSSVR) is developed through incorporating gradient/Hessian information into the traditional LSSVR. The performance of this method is tested by analytical function fitting. The experimental results illustrate that the proposed G/HELSSVR model has a great advantages over the traditional LSSVR and gradient-enhanced LSSVR (GELSSVR). Algorithms Least square support vector regression Metamodel Gradient Hessian Zhou, XiaoJian verfasserin aut Enthalten in Information processing letters Amsterdam [u.a.] : Elsevier, 1971 134, Seite 1-8 Online-Ressource (DE-627)265783771 (DE-600)1466301-6 (DE-576)074890921 1872-6119 nnns volume:134 pages:1-8 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 54.00 Informatik: Allgemeines AR 134 1-8
allfieldsSound	10.1016/j.ipl.2018.01.014 doi (DE-627)ELV00147085X (ELSEVIER)S0020-0190(18)30029-2 DE-627 ger DE-627 rda eng 004 DE-600 54.00 bkl Jiang, Ting verfasserin aut Gradient/Hessian-enhanced least square support vector regression 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In least square support vector regression (LSSVR), Vapnik's original SVR formulation has been modified by using a cost function which corresponds to a form of ridge regression rather than ε-insensitive loss function. As a result, nonlinear function estimation is done by solving linear set of equations instead of solving a time-consuming quadratic programming problem. When the gradient/Hessians in samples can be obtained cheaply, it should be considered in the construction of metamodels. In this paper, the gradient/Hessian-enhanced LSSVR (G/HELSSVR) is developed through incorporating gradient/Hessian information into the traditional LSSVR. The performance of this method is tested by analytical function fitting. The experimental results illustrate that the proposed G/HELSSVR model has a great advantages over the traditional LSSVR and gradient-enhanced LSSVR (GELSSVR). Algorithms Least square support vector regression Metamodel Gradient Hessian Zhou, XiaoJian verfasserin aut Enthalten in Information processing letters Amsterdam [u.a.] : Elsevier, 1971 134, Seite 1-8 Online-Ressource (DE-627)265783771 (DE-600)1466301-6 (DE-576)074890921 1872-6119 nnns volume:134 pages:1-8 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 54.00 Informatik: Allgemeines AR 134 1-8
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author	Jiang, Ting
spellingShingle	Jiang, Ting ddc 004 bkl 54.00 misc Algorithms misc Least square support vector regression misc Metamodel misc Gradient misc Hessian Gradient/Hessian-enhanced least square support vector regression
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topic_title	004 DE-600 54.00 bkl Gradient/Hessian-enhanced least square support vector regression Algorithms Least square support vector regression Metamodel Gradient Hessian
topic	ddc 004 bkl 54.00 misc Algorithms misc Least square support vector regression misc Metamodel misc Gradient misc Hessian
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title	Gradient/Hessian-enhanced least square support vector regression
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title_full	Gradient/Hessian-enhanced least square support vector regression
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title_sort	gradient/hessian-enhanced least square support vector regression
title_auth	Gradient/Hessian-enhanced least square support vector regression
abstract	In least square support vector regression (LSSVR), Vapnik's original SVR formulation has been modified by using a cost function which corresponds to a form of ridge regression rather than ε-insensitive loss function. As a result, nonlinear function estimation is done by solving linear set of equations instead of solving a time-consuming quadratic programming problem. When the gradient/Hessians in samples can be obtained cheaply, it should be considered in the construction of metamodels. In this paper, the gradient/Hessian-enhanced LSSVR (G/HELSSVR) is developed through incorporating gradient/Hessian information into the traditional LSSVR. The performance of this method is tested by analytical function fitting. The experimental results illustrate that the proposed G/HELSSVR model has a great advantages over the traditional LSSVR and gradient-enhanced LSSVR (GELSSVR).
abstractGer	In least square support vector regression (LSSVR), Vapnik's original SVR formulation has been modified by using a cost function which corresponds to a form of ridge regression rather than ε-insensitive loss function. As a result, nonlinear function estimation is done by solving linear set of equations instead of solving a time-consuming quadratic programming problem. When the gradient/Hessians in samples can be obtained cheaply, it should be considered in the construction of metamodels. In this paper, the gradient/Hessian-enhanced LSSVR (G/HELSSVR) is developed through incorporating gradient/Hessian information into the traditional LSSVR. The performance of this method is tested by analytical function fitting. The experimental results illustrate that the proposed G/HELSSVR model has a great advantages over the traditional LSSVR and gradient-enhanced LSSVR (GELSSVR).
abstract_unstemmed	In least square support vector regression (LSSVR), Vapnik's original SVR formulation has been modified by using a cost function which corresponds to a form of ridge regression rather than ε-insensitive loss function. As a result, nonlinear function estimation is done by solving linear set of equations instead of solving a time-consuming quadratic programming problem. When the gradient/Hessians in samples can be obtained cheaply, it should be considered in the construction of metamodels. In this paper, the gradient/Hessian-enhanced LSSVR (G/HELSSVR) is developed through incorporating gradient/Hessian information into the traditional LSSVR. The performance of this method is tested by analytical function fitting. The experimental results illustrate that the proposed G/HELSSVR model has a great advantages over the traditional LSSVR and gradient-enhanced LSSVR (GELSSVR).
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title_short	Gradient/Hessian-enhanced least square support vector regression
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up_date	2024-07-06T21:29:09.620Z
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As a result, nonlinear function estimation is done by solving linear set of equations instead of solving a time-consuming quadratic programming problem. When the gradient/Hessians in samples can be obtained cheaply, it should be considered in the construction of metamodels. In this paper, the gradient/Hessian-enhanced LSSVR (G/HELSSVR) is developed through incorporating gradient/Hessian information into the traditional LSSVR. The performance of this method is tested by analytical function fitting. 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Gradient/Hessian-enhanced least square support vector regression

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