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.

翻译：尽管取得了显著进展，以往的多视图无监督特征选择方法普遍存在两个局限性。首先，它们通常分别利用聚类结构或相似性结构指导特征选择，忽略了相互增益的联合建模可能性。其次，它们通常通过全局结构学习或局部结构学习来学习相似性结构，缺乏兼具全局与局部结构感知能力的图学习能力。为此，本文提出了一种联合多视图无监督特征选择与图学习（JMVFG）方法。具体而言，我们通过正交分解构建多视图特征选择，将每个目标矩阵分解为视图特异基矩阵与视图一致聚类指示矩阵。通过引入跨空间局部保持性，在投影空间中的聚类结构学习与原始空间中的相似性学习（即图学习）之间建立桥梁。此外，我们提出统一目标函数，实现聚类结构、全局与局部相似性结构、多视图一致性与不一致性的同步学习，并在此基础上开发了交替优化算法，理论证明了其收敛性。在多种真实多视图数据集上的广泛实验表明，该方法在多视图特征选择与图学习任务中均具有优越性。代码开源地址：https://github.com/huangdonghere/JMVFG。