Unsupervised feature selection techniques have shown promising results in dealing with unlabelled high-dimensional data. Laplacian graph-based techniques with \({l}_{\text{2,1}}\) -norm row-sparsity constraint have been popular for unsupervised feature selection tasks. However, the Laplacian graph fails to effectively preserve the topological structure of the data. To add insult to injury, \({l}_{\text{2,1}}\) -norm is the only slack version of \({l}_{2,o}\) -norm which cannot select exact top \(k\) features, and has sparsity limitation. Aiming to tackle these defects, we propose a Hessian regularized latent representation learning with \({l}_{\text{2,0}}\) -norm Constraint. Hessian regularization can preserve topological structure of data effectively, and \({l}_{\text{2,0}}\) -norm constraint is able to select top group of features. Additionally, the feature selection process is conducted within the learned latent representation, which not only exhibits robustness to noise but also takes into account the connectivity information among data instances. Non-negative matrix factorization of the affinity matrix is employed to model the latent representation, enabling the incorporation of sample connections in the representation. An optimization strategy is proposed based on power iteration method to solve this sparse unsupervised feature selection. Convergence of optimization algorithm is proved and experimental studies on real-world datasets are conducted. The obtained results demonstrate the effectiveness of proposed method.
