Unsupervised Feature Selection With Constrained ℓ₂,₀-Norm and Optimized Graph

In this article, we propose a novel feature selection approach, named unsupervised feature selection with constrained <inline-formula> <tex-math notation="LaTeX">\ell _{2,0} </tex-math></inline-formula>-norm (row-sparsity constrained) and optimized graph (RSOGFS), w...

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Published in:	IEEE transaction on neural networks and learning systems Vol. 33; no. 4; pp. 1702 - 1713
Main Authors:	Nie, Feiping, Dong, Xia, Tian, Lai, Wang, Rong, Li, Xuelong
Format:	Journal Article
Language:	English
Published:	United States IEEE 01.04.2022 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithms Approximation Approximation algorithms Computer applications Feature extraction Feature selection group feature selection Image color analysis Manifolds Mathematical analysis Noise measurement norm Objective function Optimization optimized graph Regularization Similarity Sparse matrices Sparsity unsupervised learning
ISSN:	2162-237X, 2162-2388, 2162-2388
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Abstract	In this article, we propose a novel feature selection approach, named unsupervised feature selection with constrained <inline-formula> <tex-math notation="LaTeX">\ell _{2,0} </tex-math></inline-formula>-norm (row-sparsity constrained) and optimized graph (RSOGFS), which unifies feature selection and similarity matrix construction into a general framework instead of independently performing the two-stage process; thus, the similarity matrix preserving the local manifold structure of data can be determined adaptively. Unlike those sparse learning-based feature selection methods that can only solve the relaxation or approximation problems by introducing sparsity regularization term into the objective function, the proposed method directly tackles the original <inline-formula> <tex-math notation="LaTeX">\ell _{2,0} </tex-math></inline-formula>-norm constrained problem to achieve group feature selection. Two optimization strategies are provided to solve the original sparse constrained problem. The convergence and approximation guarantees for the new algorithms are rigorously proved, and the computational complexity and parameter determination are theoretically analyzed. Experimental results on real-world data sets show that the proposed method for solving a nonconvex problem is superior to the state of the arts for solving the relaxed or approximate convex problems.
AbstractList	In this article, we propose a novel feature selection approach, named unsupervised feature selection with constrained <inline-formula> <tex-math notation="LaTeX">\ell _{2,0} </tex-math></inline-formula>-norm (row-sparsity constrained) and optimized graph (RSOGFS), which unifies feature selection and similarity matrix construction into a general framework instead of independently performing the two-stage process; thus, the similarity matrix preserving the local manifold structure of data can be determined adaptively. Unlike those sparse learning-based feature selection methods that can only solve the relaxation or approximation problems by introducing sparsity regularization term into the objective function, the proposed method directly tackles the original <inline-formula> <tex-math notation="LaTeX">\ell _{2,0} </tex-math></inline-formula>-norm constrained problem to achieve group feature selection. Two optimization strategies are provided to solve the original sparse constrained problem. The convergence and approximation guarantees for the new algorithms are rigorously proved, and the computational complexity and parameter determination are theoretically analyzed. Experimental results on real-world data sets show that the proposed method for solving a nonconvex problem is superior to the state of the arts for solving the relaxed or approximate convex problems. In this article, we propose a novel feature selection approach, named unsupervised feature selection with constrained l2,0 -norm (row-sparsity constrained) and optimized graph (RSOGFS), which unifies feature selection and similarity matrix construction into a general framework instead of independently performing the two-stage process; thus, the similarity matrix preserving the local manifold structure of data can be determined adaptively. Unlike those sparse learning-based feature selection methods that can only solve the relaxation or approximation problems by introducing sparsity regularization term into the objective function, the proposed method directly tackles the original l2,0 -norm constrained problem to achieve group feature selection. Two optimization strategies are provided to solve the original sparse constrained problem. The convergence and approximation guarantees for the new algorithms are rigorously proved, and the computational complexity and parameter determination are theoretically analyzed. Experimental results on real-world data sets show that the proposed method for solving a nonconvex problem is superior to the state of the arts for solving the relaxed or approximate convex problems.In this article, we propose a novel feature selection approach, named unsupervised feature selection with constrained l2,0 -norm (row-sparsity constrained) and optimized graph (RSOGFS), which unifies feature selection and similarity matrix construction into a general framework instead of independently performing the two-stage process; thus, the similarity matrix preserving the local manifold structure of data can be determined adaptively. Unlike those sparse learning-based feature selection methods that can only solve the relaxation or approximation problems by introducing sparsity regularization term into the objective function, the proposed method directly tackles the original l2,0 -norm constrained problem to achieve group feature selection. Two optimization strategies are provided to solve the original sparse constrained problem. The convergence and approximation guarantees for the new algorithms are rigorously proved, and the computational complexity and parameter determination are theoretically analyzed. Experimental results on real-world data sets show that the proposed method for solving a nonconvex problem is superior to the state of the arts for solving the relaxed or approximate convex problems. In this article, we propose a novel feature selection approach, named unsupervised feature selection with constrained ℓ2,0-norm (row-sparsity constrained) and optimized graph (RSOGFS), which unifies feature selection and similarity matrix construction into a general framework instead of independently performing the two-stage process; thus, the similarity matrix preserving the local manifold structure of data can be determined adaptively. Unlike those sparse learning-based feature selection methods that can only solve the relaxation or approximation problems by introducing sparsity regularization term into the objective function, the proposed method directly tackles the original ℓ2,0-norm constrained problem to achieve group feature selection. Two optimization strategies are provided to solve the original sparse constrained problem. The convergence and approximation guarantees for the new algorithms are rigorously proved, and the computational complexity and parameter determination are theoretically analyzed. Experimental results on real-world data sets show that the proposed method for solving a nonconvex problem is superior to the state of the arts for solving the relaxed or approximate convex problems. In this article, we propose a novel feature selection approach, named unsupervised feature selection with constrained [Formula Omitted]-norm (row-sparsity constrained) and optimized graph (RSOGFS), which unifies feature selection and similarity matrix construction into a general framework instead of independently performing the two-stage process; thus, the similarity matrix preserving the local manifold structure of data can be determined adaptively. Unlike those sparse learning-based feature selection methods that can only solve the relaxation or approximation problems by introducing sparsity regularization term into the objective function, the proposed method directly tackles the original [Formula Omitted]-norm constrained problem to achieve group feature selection. Two optimization strategies are provided to solve the original sparse constrained problem. The convergence and approximation guarantees for the new algorithms are rigorously proved, and the computational complexity and parameter determination are theoretically analyzed. Experimental results on real-world data sets show that the proposed method for solving a nonconvex problem is superior to the state of the arts for solving the relaxed or approximate convex problems.
Author	Wang, Rong Li, Xuelong Tian, Lai Dong, Xia Nie, Feiping
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SubjectTerms	Algorithms Approximation Approximation algorithms Computer applications Feature extraction Feature selection group feature selection Image color analysis Manifolds Mathematical analysis Noise measurement norm Objective function Optimization optimized graph Regularization Similarity Sparse matrices Sparsity unsupervised learning
Title	Unsupervised Feature Selection With Constrained ℓ₂,₀-Norm and Optimized Graph
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