A General Matrix Function Dimensionality Reduction Framework and Extension for Manifold Learning

Many dimensionality reduction methods in the manifold learning field have the so-called small-sample-size (SSS) problem. Starting from solving the SSS problem, we first summarize the existing dimensionality reduction methods and construct a unified criterion function of these methods. Then, combinin...

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Vydáno v:	IEEE transactions on cybernetics Ročník 52; číslo 4; s. 2137 - 2148
Hlavní autoři:	Ran, Ruisheng, Feng, Ji, Zhang, Shougui, Fang, Bin
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	United States IEEE 01.04.2022 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Criteria Cybernetics Dimensionality reduction Handwriting Hyperbolic functions Laplace equations Learning systems Linear functions Machine learning manifold learning Manifolds Manifolds (mathematics) Mathematical analysis matrix function Pattern classification Principal component analysis Reduction small-sample-size (SSS) problem
ISSN:	2168-2267, 2168-2275, 2168-2275
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Abstract	Many dimensionality reduction methods in the manifold learning field have the so-called small-sample-size (SSS) problem. Starting from solving the SSS problem, we first summarize the existing dimensionality reduction methods and construct a unified criterion function of these methods. Then, combining the unified criterion with the matrix function, we propose a general matrix function dimensionality reduction framework. This framework is configurable, that is, one can select suitable functions to construct such a matrix transformation framework, and then a series of new dimensionality reduction methods can be derived from this framework. In this article, we discuss how to choose suitable functions from two aspects: 1) solving the SSS problem and 2) improving pattern classification ability. As an extension, with the inverse hyperbolic tangent function and linear function, we propose a new matrix function dimensionality reduction framework. Compared with the existing methods to solve the SSS problem, these new methods can obtain better pattern classification ability and have less computational complexity. The experimental results on handwritten digit, letters databases, and two face databases show the superiority of the new methods.
AbstractList	Many dimensionality reduction methods in the manifold learning field have the so-called small-sample-size (SSS) problem. Starting from solving the SSS problem, we first summarize the existing dimensionality reduction methods and construct a unified criterion function of these methods. Then, combining the unified criterion with the matrix function, we propose a general matrix function dimensionality reduction framework. This framework is configurable, that is, one can select suitable functions to construct such a matrix transformation framework, and then a series of new dimensionality reduction methods can be derived from this framework. In this article, we discuss how to choose suitable functions from two aspects: 1) solving the SSS problem and 2) improving pattern classification ability. As an extension, with the inverse hyperbolic tangent function and linear function, we propose a new matrix function dimensionality reduction framework. Compared with the existing methods to solve the SSS problem, these new methods can obtain better pattern classification ability and have less computational complexity. The experimental results on handwritten digit, letters databases, and two face databases show the superiority of the new methods. Many dimensionality reduction methods in the manifold learning field have the so-called small-sample-size (SSS) problem. Starting from solving the SSS problem, we first summarize the existing dimensionality reduction methods and construct a unified criterion function of these methods. Then, combining the unified criterion with the matrix function, we propose a general matrix function dimensionality reduction framework. This framework is configurable, that is, one can select suitable functions to construct such a matrix transformation framework, and then a series of new dimensionality reduction methods can be derived from this framework. In this article, we discuss how to choose suitable functions from two aspects: 1) solving the SSS problem and 2) improving pattern classification ability. As an extension, with the inverse hyperbolic tangent function and linear function, we propose a new matrix function dimensionality reduction framework. Compared with the existing methods to solve the SSS problem, these new methods can obtain better pattern classification ability and have less computational complexity. The experimental results on handwritten digit, letters databases, and two face databases show the superiority of the new methods.Many dimensionality reduction methods in the manifold learning field have the so-called small-sample-size (SSS) problem. Starting from solving the SSS problem, we first summarize the existing dimensionality reduction methods and construct a unified criterion function of these methods. Then, combining the unified criterion with the matrix function, we propose a general matrix function dimensionality reduction framework. This framework is configurable, that is, one can select suitable functions to construct such a matrix transformation framework, and then a series of new dimensionality reduction methods can be derived from this framework. In this article, we discuss how to choose suitable functions from two aspects: 1) solving the SSS problem and 2) improving pattern classification ability. As an extension, with the inverse hyperbolic tangent function and linear function, we propose a new matrix function dimensionality reduction framework. Compared with the existing methods to solve the SSS problem, these new methods can obtain better pattern classification ability and have less computational complexity. The experimental results on handwritten digit, letters databases, and two face databases show the superiority of the new methods.
Author	Ran, Ruisheng Fang, Bin Zhang, Shougui Feng, Ji
Author_xml	– sequence: 1 givenname: Ruisheng orcidid: 0000-0002-0785-2703 surname: Ran fullname: Ran, Ruisheng email: rshran@cqnu.edu.cn organization: College of Computer and Information Science, College of Intelligent Science, Chongqing Normal University, Chongqing, China – sequence: 2 givenname: Ji surname: Feng fullname: Feng, Ji email: fengji@cqnu.edu.cn organization: College of Computer and Information Science, Chongqing Normal University, Chongqing, China – sequence: 3 givenname: Shougui surname: Zhang fullname: Zhang, Shougui email: shgzhang@cqnu.edu.cn organization: School of Mathematical Science, Chongqing Normal University, Chongqing, China – sequence: 4 givenname: Bin orcidid: 0000-0003-1955-6626 surname: Fang fullname: Fang, Bin email: fb@cqu.edu.cn organization: College of Computer Science, Chongqing University, Chongqing, China
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SubjectTerms	Criteria Cybernetics Dimensionality reduction Handwriting Hyperbolic functions Laplace equations Learning systems Linear functions Machine learning manifold learning Manifolds Manifolds (mathematics) Mathematical analysis matrix function Pattern classification Principal component analysis Reduction small-sample-size (SSS) problem
Title	A General Matrix Function Dimensionality Reduction Framework and Extension for Manifold Learning
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