HLR-UFS: Hessian-based Unsupervised Feature Selection using Low-Rank Approximation.

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.