Global and local structure preserving sparse subspace learning: An iterative approach to unsupervised feature selection

As we aim at alleviating the curse of high-dimensionality, subspace learning is becoming more popular. Existing approaches use either information about global or local structure of the data, and few studies simultaneously focus on global and local structures as the both of them contain important information. In this paper, we propose a global and local structure preserving sparse subspace learning (GLoSS) model for unsupervised feature selection. The model can simultaneously realize feature selection and subspace learning. In addition, we develop a greedy algorithm to establish a generic combinatorial model, and an iterative strategy based on an accelerated block coordinate descent is used to solve the GLoSS problem. We also provide whole iterate sequence convergence analysis of the proposed iterative algorithm. Extensive experiments are conducted on real-world datasets to show the superiority of the proposed approach over several state-of-the-art unsupervised feature selection approaches. HighlightsWe propose a novel unsupervised subspace learning model for unsupervised learning.We propose a greedy algorithm to solve a combinatorial model.We propose an iterative algorithm to solve the relaxed continuous model.We establish a whole iterate sequence convergence result of the iterative algorithm.We conduct extensive experimental studies about the proposed algorithms.