Fast Unsupervised Feature Selection With Bipartite Graph and $\ell _{2,0}$ℓ2,0-Norm Constraint

Since obtaining data labels is a time-consuming and laborious task, unsupervised feature selection has become a popular feature selection technique. However, the current unsupervised feature selection methods are facing three challenges: (1) they rely on a fixed similarity matrix derived from the original data, which will affect their performance; (2) due to the limitation of sparsity, they can only obtain sub-optimal solutions; (3) they have high computational complexity and cannot handle large-scale data. To solve this dilemma, we propose a fast unsupervised feature selection algorithm with bipartite graph and
$\ell _{2,0}$
-norm constraint (BGCFS). We use the original data and the selected anchors to construct an adaptive bipartite graph in the subspace, and apply the
$\ell _{2,0}$
-norm constraint to the projection matrix for feature selection. In this way, we can update the adaptive bipartite graph and the projection matrix simultaneously, and we can get the feature subset directly, without sorting the features. In addition, we propose an iterative algorithm that can solve the proposed problem globally to obtain a closed-form solution, and we provide a strict proof of convergence for it. Experiments on eight real data sets with different scales show that our method can select more valuable feature subsets more quickly.