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Despite significant progress, previous multi-view unsupervised featureselection methods mostly suffer from two limitations. First, they generallyutilize either cluster structure or similarity structure to guide the featureselection, which neglect the possibility of a joint formulation with mutualbenefits. Second, they often learn the similarity structure by either globalstructure learning or local structure learning, which lack the capability ofgraph learning with both global and local structural awareness. In light ofthis, this paper presents a joint multi-view unsupervised feature selection andgraph learning (JMVFG) approach. Particularly, we formulate the multi-viewfeature selection with orthogonal decomposition, where each target matrix isdecomposed into a view-specific basis matrix and a view-consistent clusterindicator. The cross-space locality preservation is incorporated to bridge thecluster structure learning in the projected space and the similarity learning(i.e., graph learning) in the original space. Further, a unified objectivefunction is presented to enable the simultaneous learning of the clusterstructure, the global and local similarity structures, and the multi-viewconsistency and inconsistency, upon which an alternating optimization algorithmis developed with theoretically proved convergence. Extensive experiments on avariety of real-world multi-view datasets demonstrate the superiority of ourapproach for both the multi-view feature selection and graph learning tasks.The code is available at https://github.com/huangdonghere/JMVFG.

Joint Multi-view Unsupervised Feature Selection and Graph Learning