Block-diagonal graph embedding for unsupervised feature selection

The aim of unsupervised feature selection (UFS) is to remove irrelevant, redundant and noisy features, which could reduce the time consumption and improve the clustering performance of learning machine. Due to the absence of label information, the major research direction of UFS models lies in how to characterize the manifold structure of high-dimensional data and generate the pseudo labels for data samples properly. With the generated label information, a faithful and compact feature subset could be produced that sufficiently preserves the intrinsic structure. In this paper, we propose a novel subspace clustering guided unsupervised feature selection (BDGFS) model. Specifically, the underlying manifold structure is captured by subspace clustering method that could adaptively preserve the cluster labels, meanwhile the salient features are selected to dominate the projected subspace. The BDGFS model can naturally preserve the multi-subspace distribution via subspace clustering and simultaneously learn the feature weight matrix which is sufficient to characterize the underling subspace structure with exact components preserving. We develop an alternative optimization strategy to solve the challenging objective function, and then discuss the convergence of the proposed algorithm. Experimental results on benchmark databases demonstrate that the BDGFS model could outperform the state-of-the-art UFS models. The code of the BDGFS model is released at https://github.com/ty-kj/BDGFS.