HLR-UFS: Hessian-based Unsupervised Feature Selection using Low-Rank Approximation
- 1College of Mathematics and Information Engineering, Longyan University, Longyan, China
- 2Fujian Provincial University Key Laboratory of Big Data Mining and Applications, Longyan University, Longyan, China
Abstract
Graph-based Laplacian regularization techniques have been extensively applied in unsupervised feature selection due to their capability in capturing the inherent structure of data. However, Laplacian regularization frequently results in a solution that is biased towards a constant geodesic function, which leads to inadequate extrapolation capabilities and an inability to robustly maintain the data’s topological structure. Aiming to tackle the drawback, we propose a new framework named Hessian-based Unsupervised Feature Selection using Low-Rank Approximation (HLR-UFS). First, our method introduces Hessian regularization to address the inability of graph-based Laplacian regularization to effectively preserve complex topological structures and nonlinear geometric information due to null space constraints. Second, to explicitly eliminate feature redundancy, we use low-rank approximation techniques to identify latent correlations among features. Furthermore, we employ ℓ2,1-norm regularization to suppress noise and outliers. Finally, we design an efficient algorithm and rigorously validate its convergence through theoretical analysis. Comprehensive assessments on nine standard datasets show the validity and superior performance of HLR-UFS.
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BibTeX
@article{zhang2026hlrufs,
title = {{HLR-UFS: Hessian-based Unsupervised Feature Selection using Low-Rank Approximation}},
author = {Jiyan Zhang and Weihan Lin and Yanfang Liu and Shuzhen Tu and Ming Peng},
journal = {PLOS One},
year = {2026},
month = sep,
doi = {10.1371/journal.pone.0356837},
url = {https://doi.org/10.1371/journal.pone.0356837},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - HLR-UFS: Hessian-based Unsupervised Feature Selection using Low-Rank Approximation
AU - Jiyan Zhang
AU - Weihan Lin
AU - Yanfang Liu
AU - Shuzhen Tu
AU - Ming Peng
PY - 2026
DA - 2026/09/03
JO - PLOS One
DO - 10.1371/journal.pone.0356837
UR - https://doi.org/10.1371/journal.pone.0356837
AB - Graph-based Laplacian regularization techniques have been extensively applied in unsupervised feature selection due to their capability in capturing the inherent structure of data. However, Laplacian regularization frequently results in a solution that is biased towards a constant geodesic function, which leads to inadequate extrapolation capabilities and an inability to robustly maintain the data’s topological structure. Aiming to tackle the drawback, we propose a new framework named Hessian-based Unsupervised Feature Selection using Low-Rank Approximation (HLR-UFS). First, our method introduces Hessian regularization to address the inability of graph-based Laplacian regularization to effectively preserve complex topological structures and nonlinear geometric information due to null space constraints. Second, to explicitly eliminate feature redundancy, we use low-rank approximation techniques to identify latent correlations among features. Furthermore, we employ ℓ2,1-norm regularization to suppress noise and outliers. Finally, we design an efficient algorithm and rigorously validate its convergence through theoretical analysis. Comprehensive assessments on nine standard datasets show the validity and superior performance of HLR-UFS.
SN - 1932-6203
ER -