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