Top-k Feature Selection Framework Using Robust 0-1 Integer Programming

Feature selection (FS), which identifies the relevant features in a data set to facilitate subsequent data analysis, is a fundamental problem in machine learning and has been widely studied in recent years. Most FS methods rank the features in order of their scores based on a specific criterion and...

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Published in:	IEEE transaction on neural networks and learning systems Vol. 32; no. 7; pp. 3005 - 3019
Main Authors:	Zhang, Xiaoqin, Fan, Mingyu, Wang, Di, Zhou, Peng, Tao, Dacheng
Format:	Journal Article
Language:	English
Published:	Piscataway IEEE 01.07.2021 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	0-1 integer programming Computer science Constraints Correlation Data analysis Datasets Equivalence Fans Feature extraction Feature selection feature selection (FS) Integer programming Learning algorithms Linear programming Machine learning nonconvex optimization norm Optimization Robustness
ISSN:	2162-237X, 2162-2388, 2162-2388
Online Access:	Get full text
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Abstract	Feature selection (FS), which identifies the relevant features in a data set to facilitate subsequent data analysis, is a fundamental problem in machine learning and has been widely studied in recent years. Most FS methods rank the features in order of their scores based on a specific criterion and then select the <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> top-ranked features, where <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> is the number of desired features. However, these features are usually not the top-<inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> features and may present a suboptimal choice. To address this issue, we propose a novel FS framework in this article to select the exact top-<inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> features in the unsupervised, semisupervised, and supervised scenarios. The new framework utilizes the <inline-formula> <tex-math notation="LaTeX">\ell _{0,2} </tex-math></inline-formula>-norm as the matrix sparsity constraint rather than its relaxations, such as the <inline-formula> <tex-math notation="LaTeX">\ell _{1,2} </tex-math></inline-formula>-norm. Since the <inline-formula> <tex-math notation="LaTeX">\ell _{0,2} </tex-math></inline-formula>-norm constrained problem is difficult to solve, we transform the discrete <inline-formula> <tex-math notation="LaTeX">\ell _{0,2} </tex-math></inline-formula>-norm-based constraint into an equivalent 0-1 integer constraint and replace the 0-1 integer constraint with two continuous constraints. The obtained top-<inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> FS framework with two continuous constraints is theoretically equivalent to the <inline-formula> <tex-math notation="LaTeX">\ell _{0,2} </tex-math></inline-formula>-norm constrained problem and can be optimized by the alternating direction method of multipliers (ADMM). Unsupervised and semisupervised FS methods are developed based on the proposed framework, and extensive experiments on real-world data sets are conducted to demonstrate the effectiveness of the proposed FS framework.
AbstractList	Feature selection (FS), which identifies the relevant features in a data set to facilitate subsequent data analysis, is a fundamental problem in machine learning and has been widely studied in recent years. Most FS methods rank the features in order of their scores based on a specific criterion and then select the <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> top-ranked features, where <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> is the number of desired features. However, these features are usually not the top-<inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> features and may present a suboptimal choice. To address this issue, we propose a novel FS framework in this article to select the exact top-<inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> features in the unsupervised, semisupervised, and supervised scenarios. The new framework utilizes the <inline-formula> <tex-math notation="LaTeX">\ell _{0,2} </tex-math></inline-formula>-norm as the matrix sparsity constraint rather than its relaxations, such as the <inline-formula> <tex-math notation="LaTeX">\ell _{1,2} </tex-math></inline-formula>-norm. Since the <inline-formula> <tex-math notation="LaTeX">\ell _{0,2} </tex-math></inline-formula>-norm constrained problem is difficult to solve, we transform the discrete <inline-formula> <tex-math notation="LaTeX">\ell _{0,2} </tex-math></inline-formula>-norm-based constraint into an equivalent 0-1 integer constraint and replace the 0-1 integer constraint with two continuous constraints. The obtained top-<inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> FS framework with two continuous constraints is theoretically equivalent to the <inline-formula> <tex-math notation="LaTeX">\ell _{0,2} </tex-math></inline-formula>-norm constrained problem and can be optimized by the alternating direction method of multipliers (ADMM). Unsupervised and semisupervised FS methods are developed based on the proposed framework, and extensive experiments on real-world data sets are conducted to demonstrate the effectiveness of the proposed FS framework. Feature selection (FS), which identifies the relevant features in a data set to facilitate subsequent data analysis, is a fundamental problem in machine learning and has been widely studied in recent years. Most FS methods rank the features in order of their scores based on a specific criterion and then select the [Formula Omitted] top-ranked features, where [Formula Omitted] is the number of desired features. However, these features are usually not the top-[Formula Omitted] features and may present a suboptimal choice. To address this issue, we propose a novel FS framework in this article to select the exact top-[Formula Omitted] features in the unsupervised, semisupervised, and supervised scenarios. The new framework utilizes the [Formula Omitted]-norm as the matrix sparsity constraint rather than its relaxations, such as the [Formula Omitted]-norm. Since the [Formula Omitted]-norm constrained problem is difficult to solve, we transform the discrete [Formula Omitted]-norm-based constraint into an equivalent 0–1 integer constraint and replace the 0–1 integer constraint with two continuous constraints. The obtained top-[Formula Omitted] FS framework with two continuous constraints is theoretically equivalent to the [Formula Omitted]-norm constrained problem and can be optimized by the alternating direction method of multipliers (ADMM). Unsupervised and semisupervised FS methods are developed based on the proposed framework, and extensive experiments on real-world data sets are conducted to demonstrate the effectiveness of the proposed FS framework. Feature selection (FS), which identifies the relevant features in a data set to facilitate subsequent data analysis, is a fundamental problem in machine learning and has been widely studied in recent years. Most FS methods rank the features in order of their scores based on a specific criterion and then select the k top-ranked features, where k is the number of desired features. However, these features are usually not the top- k features and may present a suboptimal choice. To address this issue, we propose a novel FS framework in this article to select the exact top- k features in the unsupervised, semisupervised, and supervised scenarios. The new framework utilizes the l0,2 -norm as the matrix sparsity constraint rather than its relaxations, such as the l1,2 -norm. Since the l0,2 -norm constrained problem is difficult to solve, we transform the discrete l0,2 -norm-based constraint into an equivalent 0-1 integer constraint and replace the 0-1 integer constraint with two continuous constraints. The obtained top- k FS framework with two continuous constraints is theoretically equivalent to the l0,2 -norm constrained problem and can be optimized by the alternating direction method of multipliers (ADMM). Unsupervised and semisupervised FS methods are developed based on the proposed framework, and extensive experiments on real-world data sets are conducted to demonstrate the effectiveness of the proposed FS framework.Feature selection (FS), which identifies the relevant features in a data set to facilitate subsequent data analysis, is a fundamental problem in machine learning and has been widely studied in recent years. Most FS methods rank the features in order of their scores based on a specific criterion and then select the k top-ranked features, where k is the number of desired features. However, these features are usually not the top- k features and may present a suboptimal choice. To address this issue, we propose a novel FS framework in this article to select the exact top- k features in the unsupervised, semisupervised, and supervised scenarios. The new framework utilizes the l0,2 -norm as the matrix sparsity constraint rather than its relaxations, such as the l1,2 -norm. Since the l0,2 -norm constrained problem is difficult to solve, we transform the discrete l0,2 -norm-based constraint into an equivalent 0-1 integer constraint and replace the 0-1 integer constraint with two continuous constraints. The obtained top- k FS framework with two continuous constraints is theoretically equivalent to the l0,2 -norm constrained problem and can be optimized by the alternating direction method of multipliers (ADMM). Unsupervised and semisupervised FS methods are developed based on the proposed framework, and extensive experiments on real-world data sets are conducted to demonstrate the effectiveness of the proposed FS framework.
Author	Tao, Dacheng Wang, Di Zhang, Xiaoqin Zhou, Peng Fan, Mingyu
Author_xml	– sequence: 1 givenname: Xiaoqin orcidid: 0000-0003-0958-7285 surname: Zhang fullname: Zhang, Xiaoqin email: zhangxiaoqinnan@gmail.com organization: College of Computer Science and Artificial Intelligence, Wenzhou University, Wenzhou, China – sequence: 2 givenname: Mingyu orcidid: 0000-0002-0492-4708 surname: Fan fullname: Fan, Mingyu email: fanmingyu@wzu.edu.cn organization: College of Computer Science and Artificial Intelligence, Wenzhou University, Wenzhou, China – sequence: 3 givenname: Di orcidid: 0000-0003-0435-0609 surname: Wang fullname: Wang, Di email: wang.di@xjtu.edu.cn organization: Center of Intelligent Decision-Making and Machine Learning, School of Management, Xi'an Jiaotong University, Xi'an, China – sequence: 4 givenname: Peng orcidid: 0000-0002-3675-4985 surname: Zhou fullname: Zhou, Peng email: zhoupeng@ahu.edu.cn organization: School of Computer Science and Technology, Anhui University, Hefei, China – sequence: 5 givenname: Dacheng orcidid: 0000-0001-7225-5449 surname: Tao fullname: Tao, Dacheng email: dacheng.tao@sydney.edu.au organization: UBTECH Sydney Artificial Intelligence Centre and the School of Computer Science, Faculty of Engineering, The University of Sydney, Darlington, NSW, Australia
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Snippet	Feature selection (FS), which identifies the relevant features in a data set to facilitate subsequent data analysis, is a fundamental problem in machine...
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SubjectTerms	0-1 integer programming Computer science Constraints Correlation Data analysis Datasets Equivalence Fans Feature extraction Feature selection feature selection (FS) Integer programming Learning algorithms Linear programming Machine learning nonconvex optimization norm Optimization Robustness
Title	Top-k Feature Selection Framework Using Robust 0-1 Integer Programming
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