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，以往的多视角无监督特征选择方法仍存在两个主要局限。首先，它们通常仅利用聚类结构或相似性结构来指导特征选择，忽视了二者联合建模可能带来的互惠效应。其次，它们往往通过全局结构学习或局部结构学习来构建相似性结构，缺乏同时具备全局与局部结构感知能力的图学习机制。鉴于此，本文提出一种联合多视角无监督特征选择与图学习（JMVFG）方法。具体而言，我们通过正交分解对多视角特征选择进行建模，将每个目标矩阵分解为视角特定基矩阵与视角一致聚类指示矩阵。通过引入跨空间局部性保持机制，桥接了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）。进一步地，我们构建了统一的目标函数，使聚类结构、全局与局部相似性结构以及多视角一致性与不一致性能够同时学习，并据此设计了交替优化算法，其收敛性得到理论证明。在多种真实世界多视角数据集上的大量实验表明，我们方法在多视角特征选择与图学习任务中均具有优越性。相关代码已开源在 https://github.com/huangdonghere/JMVFG。