Joint Structured Bipartite Graph and Row-Sparse Projection for Large-Scale Feature Selection

Feature selection plays an important role in data analysis, yet traditional graph-based methods often produce suboptimal results. These methods typically follow a two-stage process: constructing a graph with data-to-data affinities or a bipartite graph with data-to-anchor affinities and independently selecting features based on their scores. In this article, a large-scale feature selection approach based on structured bipartite graph and row-sparse projection (RS $^2$ BLFS) is proposed to overcome this limitation. RS $^2$ BLFS integrates the construction of a structured bipartite graph consisting of $c$ connected components into row-sparse projection learning with $k$ nonzero rows. This integration allows for the joint selection of an optimal feature subset in an unsupervised manner. Notably, the $c$ connected components of the structured bipartite graph correspond to $c$ clusters, each with multiple subcluster centers. This feature makes RS $^2$ BLFS particularly effective for feature selection and clustering on nonspherical large-scale data. An algorithm with theoretical analysis is developed to solve the optimization problem involved in RS $^2$ BLFS. Experimental results on synthetic and real-world datasets confirm its effectiveness in feature selection tasks.