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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Veröffentlicht in:IEEE transaction on neural networks and learning systems Jg. 33; H. 4; S. 1702 - 1713
Hauptverfasser: Nie, Feiping, Dong, Xia, Tian, Lai, Wang, Rong, Li, Xuelong
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States IEEE 01.04.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
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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Zusammenfassung: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.
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ISSN:2162-237X
2162-2388
2162-2388
DOI:10.1109/TNNLS.2020.3043362