Joint Multi-View Unsupervised Feature Selection and Graph Learning

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 article presents a
j
oint
m
ulti-
v
iew unsupervised
f
eature selection and
g
raph 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
.