Subspace Learning for Dual High-Order Graph Learning Based on Boolean Weight

Subspace learning has achieved promising performance as a key technique for unsupervised feature selection. The strength of subspace learning lies in its ability to identify a representative subspace encompassing a cluster of features that are capable of effectively approximating the space of the original features. Nonetheless, most existing unsupervised feature selection methods based on subspace learning are constrained by two primary challenges. (1) Many methods only predominantly focus on the relationships between samples in the data space but ignore the correlated information between features in the feature space, which is unreliable for exploiting the intrinsic spatial structure. (2) Graph-based methods typically only take account of one-order neighborhood structures, neglecting high-order neighborhood structures inherent in original data, thereby failing to accurately preserve local geometric characteristics of the data. To pursue filling this gap in research, taking dual high-order graph learning into account, we propose a framework called subspace learning for dual high-order graph learning based on Boolean weight (DHBWSL). Firstly, a framework for unsupervised feature selection based on subspace learning is proposed, which is extended by dual-graph regularization to fully investigate geometric structure information on dual spaces. Secondly, the dual high-order graph is designed by embedding Boolean weights to learn a more extensive node from the original space such that the appropriate high-order adjacency matrix can be selected adaptively and flexibly. Experimental results on 12 public datasets demonstrate that the proposed DHBWSL outperforms the nine recent state-of-the-art algorithms.