Soft Margin Multiple Kernel Learning

Multiple kernel learning (MKL) has been proposed for kernel methods by learning the optimal kernel from a set of predefined base kernels. However, the traditional L 1 MKL method often achieves worse results than the simplest method using the average of base kernels (i.e., average kernel) in some pra...

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Veröffentlicht in:	IEEE transaction on neural networks and learning systems Jg. 24; H. 5; S. 749 - 761
Hauptverfasser:	Xinxing Xu, Tsang, I. W., Dong Xu
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York, NY IEEE 01.05.2013 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Algorithms Applied sciences Artificial intelligence Computer science; control theory; systems Data processing. List processing. Character string processing Exact sciences and technology Fasteners Hinges Kernel Kernels Learning Learning and adaptive systems Linear programming Mathematical models Memory organisation. Data processing Multiple kernel learning Neural networks Operations research Optimization Pattern recognition. Digital image processing. Computational geometry Recognition Software Studies Support vector machines Training Vectors Multiple kernel learning Action Event detection support vector machines Motion estimation Video signal Modeling Kernel method Loss function Behavioral analysis Efficiency Scene analysis Vector support machine Objective function Learning algorithm Single machine
ISSN:	2162-237X, 2162-2388, 2162-2388
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Abstract	Multiple kernel learning (MKL) has been proposed for kernel methods by learning the optimal kernel from a set of predefined base kernels. However, the traditional L 1 MKL method often achieves worse results than the simplest method using the average of base kernels (i.e., average kernel) in some practical applications. In order to improve the effectiveness of MKL, this paper presents a novel soft margin perspective for MKL. Specifically, we introduce an additional slack variable called kernel slack variable to each quadratic constraint of MKL, which corresponds to one support vector machine model using a single base kernel. We first show that L 1 MKL can be deemed as hard margin MKL, and then we propose a novel soft margin framework for MKL. Three commonly used loss functions, including the hinge loss, the square hinge loss, and the square loss, can be readily incorporated into this framework, leading to the new soft margin MKL objective functions. Many existing MKL methods can be shown as special cases under our soft margin framework. For example, the hinge loss soft margin MKL leads to a new box constraint for kernel combination coefficients. Using different hyper-parameter values for this formulation, we can inherently bridge the method using average kernel, L 1 MKL, and the hinge loss soft margin MKL. The square hinge loss soft margin MKL unifies the family of elastic net constraint/regularizer based approaches; and the square loss soft margin MKL incorporates L 2 MKL naturally. Moreover, we also develop efficient algorithms for solving both the hinge loss and square hinge loss soft margin MKL. Comprehensive experimental studies for various MKL algorithms on several benchmark data sets and two real world applications, including video action recognition and event recognition demonstrate that our proposed algorithms can efficiently achieve an effective yet sparse solution for MKL.
AbstractList	Multiple kernel learning (MKL) has been proposed for kernel methods by learning the optimal kernel from a set of predefined base kernels. However, the traditional L1MKL method often achieves worse results than the simplest method using the average of base kernels (i.e., average kernel) in some practical applications. In order to improve the effectiveness of MKL, this paper presents a novel soft margin perspective for MKL. Specifically, we introduce an additional slack variable called kernel slack variable to each quadratic constraint of MKL, which corresponds to one support vector machine model using a single base kernel. We first show that L1MKL can be deemed as hard margin MKL, and then we propose a novel soft margin framework for MKL. Three commonly used loss functions, including the hinge loss, the square hinge loss, and the square loss, can be readily incorporated into this framework, leading to the new soft margin MKL objective functions. Many existing MKL methods can be shown as special cases under our soft margin framework. For example, the hinge loss soft margin MKL leads to a new box constraint for kernel combination coefficients. Using different hyper-parameter values for this formulation, we can inherently bridge the method using average kernel, L1MKL, and the hinge loss soft margin MKL. The square hinge loss soft margin MKL unifies the family of elastic net constraint/regularizer based approaches; and the square loss soft margin MKL incorporates L2MKL naturally. Moreover, we also develop efficient algorithms for solving both the hinge loss and square hinge loss soft margin MKL. Comprehensive experimental studies for various MKL algorithms on several benchmark data sets and two real world applications, including video action recognition and event recognition demonstrate that our proposed algorithms can efficiently achieve an effective yet sparse solution for MKL.Multiple kernel learning (MKL) has been proposed for kernel methods by learning the optimal kernel from a set of predefined base kernels. However, the traditional L1MKL method often achieves worse results than the simplest method using the average of base kernels (i.e., average kernel) in some practical applications. In order to improve the effectiveness of MKL, this paper presents a novel soft margin perspective for MKL. Specifically, we introduce an additional slack variable called kernel slack variable to each quadratic constraint of MKL, which corresponds to one support vector machine model using a single base kernel. We first show that L1MKL can be deemed as hard margin MKL, and then we propose a novel soft margin framework for MKL. Three commonly used loss functions, including the hinge loss, the square hinge loss, and the square loss, can be readily incorporated into this framework, leading to the new soft margin MKL objective functions. Many existing MKL methods can be shown as special cases under our soft margin framework. For example, the hinge loss soft margin MKL leads to a new box constraint for kernel combination coefficients. Using different hyper-parameter values for this formulation, we can inherently bridge the method using average kernel, L1MKL, and the hinge loss soft margin MKL. The square hinge loss soft margin MKL unifies the family of elastic net constraint/regularizer based approaches; and the square loss soft margin MKL incorporates L2MKL naturally. Moreover, we also develop efficient algorithms for solving both the hinge loss and square hinge loss soft margin MKL. Comprehensive experimental studies for various MKL algorithms on several benchmark data sets and two real world applications, including video action recognition and event recognition demonstrate that our proposed algorithms can efficiently achieve an effective yet sparse solution for MKL. Multiple kernel learning (MKL) has been proposed for kernel methods by learning the optimal kernel from a set of predefined base kernels. However, the traditional L 1 rm MKL method often achieves worse results than the simplest method using the average of base kernels (i.e., average kernel) in some practical applications. In order to improve the effectiveness of MKL, this paper presents a novel soft margin perspective for MKL. Specifically, we introduce an additional slack variable called kernel slack variable to each quadratic constraint of MKL, which corresponds to one support vector machine model using a single base kernel. We first show that L 1 rm MKL can be deemed as hard margin MKL, and then we propose a novel soft margin framework for MKL. Three commonly used loss functions, including the hinge loss, the square hinge loss, and the square loss, can be readily incorporated into this framework, leading to the new soft margin MKL objective functions. Many existing MKL methods can be shown as special cases under our soft margin framework. For example, the hinge loss soft margin MKL leads to a new box constraint for kernel combination coefficients. Using different hyper-parameter values for this formulation, we can inherently bridge the method using average kernel, L 1 rm MKL , and the hinge loss soft margin MKL. The square hinge loss soft margin MKL unifies the family of elastic net constraint/regularizer based approaches; and the square loss soft margin MKL incorporates L 2 rm MKL naturally. Moreover, we also develop efficient algorithms for solving both the hinge loss and square hinge loss soft margin MKL. Comprehensive experimental studies for various MKL algorithms on several benchmark data sets and two real world applications, including video action recognition and event recognition demonstrate that our proposed algorithms can efficiently achieve an effective yet sparse solution for MKL. Multiple kernel learning (MKL) has been proposed for kernel methods by learning the optimal kernel from a set of predefined base kernels. However, the traditional [Formula Omitted] method often achieves worse results than the simplest method using the average of base kernels (i.e., average kernel) in some practical applications. In order to improve the effectiveness of MKL, this paper presents a novel soft margin perspective for MKL. Specifically, we introduce an additional slack variable called kernel slack variable to each quadratic constraint of MKL, which corresponds to one support vector machine model using a single base kernel. We first show that [Formula Omitted] can be deemed as hard margin MKL, and then we propose a novel soft margin framework for MKL. Three commonly used loss functions, including the hinge loss, the square hinge loss, and the square loss, can be readily incorporated into this framework, leading to the new soft margin MKL objective functions. Many existing MKL methods can be shown as special cases under our soft margin framework. For example, the hinge loss soft margin MKL leads to a new box constraint for kernel combination coefficients. Using different hyper-parameter values for this formulation, we can inherently bridge the method using average kernel, [Formula Omitted], and the hinge loss soft margin MKL. The square hinge loss soft margin MKL unifies the family of elastic net constraint/regularizer based approaches; and the square loss soft margin MKL incorporates [Formula Omitted] naturally. Moreover, we also develop efficient algorithms for solving both the hinge loss and square hinge loss soft margin MKL. Comprehensive experimental studies for various MKL algorithms on several benchmark data sets and two real world applications, including video action recognition and event recognition demonstrate that our proposed algorithms can efficiently achieve an effective yet sparse solution for MKL. Multiple kernel learning (MKL) has been proposed for kernel methods by learning the optimal kernel from a set of predefined base kernels. However, the traditional L1MKL method often achieves worse results than the simplest method using the average of base kernels (i.e., average kernel) in some practical applications. In order to improve the effectiveness of MKL, this paper presents a novel soft margin perspective for MKL. Specifically, we introduce an additional slack variable called kernel slack variable to each quadratic constraint of MKL, which corresponds to one support vector machine model using a single base kernel. We first show that L1MKL can be deemed as hard margin MKL, and then we propose a novel soft margin framework for MKL. Three commonly used loss functions, including the hinge loss, the square hinge loss, and the square loss, can be readily incorporated into this framework, leading to the new soft margin MKL objective functions. Many existing MKL methods can be shown as special cases under our soft margin framework. For example, the hinge loss soft margin MKL leads to a new box constraint for kernel combination coefficients. Using different hyper-parameter values for this formulation, we can inherently bridge the method using average kernel, L1MKL, and the hinge loss soft margin MKL. The square hinge loss soft margin MKL unifies the family of elastic net constraint/regularizer based approaches; and the square loss soft margin MKL incorporates L2MKL naturally. Moreover, we also develop efficient algorithms for solving both the hinge loss and square hinge loss soft margin MKL. Comprehensive experimental studies for various MKL algorithms on several benchmark data sets and two real world applications, including video action recognition and event recognition demonstrate that our proposed algorithms can efficiently achieve an effective yet sparse solution for MKL. Multiple kernel learning (MKL) has been proposed for kernel methods by learning the optimal kernel from a set of predefined base kernels. However, the traditional L 1 MKL method often achieves worse results than the simplest method using the average of base kernels (i.e., average kernel) in some practical applications. In order to improve the effectiveness of MKL, this paper presents a novel soft margin perspective for MKL. Specifically, we introduce an additional slack variable called kernel slack variable to each quadratic constraint of MKL, which corresponds to one support vector machine model using a single base kernel. We first show that L 1 MKL can be deemed as hard margin MKL, and then we propose a novel soft margin framework for MKL. Three commonly used loss functions, including the hinge loss, the square hinge loss, and the square loss, can be readily incorporated into this framework, leading to the new soft margin MKL objective functions. Many existing MKL methods can be shown as special cases under our soft margin framework. For example, the hinge loss soft margin MKL leads to a new box constraint for kernel combination coefficients. Using different hyper-parameter values for this formulation, we can inherently bridge the method using average kernel, L 1 MKL, and the hinge loss soft margin MKL. The square hinge loss soft margin MKL unifies the family of elastic net constraint/regularizer based approaches; and the square loss soft margin MKL incorporates L 2 MKL naturally. Moreover, we also develop efficient algorithms for solving both the hinge loss and square hinge loss soft margin MKL. Comprehensive experimental studies for various MKL algorithms on several benchmark data sets and two real world applications, including video action recognition and event recognition demonstrate that our proposed algorithms can efficiently achieve an effective yet sparse solution for MKL.
Author	Xinxing Xu Tsang, I. W. Dong Xu
Author_xml	– sequence: 1 surname: Xinxing Xu fullname: Xinxing Xu organization: Sch. of Comput. Eng., Nanyang Technol. Univ., Singapore, Singapore – sequence: 2 givenname: I. W. surname: Tsang fullname: Tsang, I. W. organization: Sch. of Comput. Eng., Nanyang Technol. Univ., Singapore, Singapore – sequence: 3 surname: Dong Xu fullname: Dong Xu organization: Sch. of Comput. Eng., Nanyang Technol. Univ., Singapore, Singapore
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Keywords	Multiple kernel learning Action Event detection support vector machines Motion estimation Video signal Modeling Kernel method Loss function Behavioral analysis Efficiency Scene analysis Vector support machine Objective function Learning algorithm Single machine
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Snippet	Multiple kernel learning (MKL) has been proposed for kernel methods by learning the optimal kernel from a set of predefined base kernels. However, the...
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SubjectTerms	Algorithms Applied sciences Artificial intelligence Computer science; control theory; systems Data processing. List processing. Character string processing Exact sciences and technology Fasteners Hinges Kernel Kernels Learning Learning and adaptive systems Linear programming Mathematical models Memory organisation. Data processing Multiple kernel learning Neural networks Operations research Optimization Pattern recognition. Digital image processing. Computational geometry Recognition Software Studies Support vector machines Training Vectors
Title	Soft Margin Multiple Kernel Learning
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