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 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.

I. Introduction

The rapid development of information technology gives rise to the mass emergence of high-dimensional data, which can be collected from different sources (or views) and have brought significant challenges to the field of computational intelligence and machine learning. In particular, due to the scarcity of true labels in massive data, the unsupervised learning has recently emerged as a promising direction, where the unsupervised feature selection [1] and the clustering analysis [2] may be two of the most popular topics. Although extensive studies have been conducted on each of them, yet surprisingly few efforts have been devoted to the simultaneous and unified modeling of these two research topics for multi-view high-dimensional data. In view of this, this article focuses on the intersection of multi-view unsupervised feature selection and multi-view clustering (especially via graph learning).