Multi-view subspace clustering algorithms have recently been developed to process multi-view dataset clustering by accurately depicting the essential characteristics of multi-view data. Most existing methods focus on conduct self-representation property using a consistent representation and a set of specific representations with well-designed regularization to learn the common and specific knowledge among different views. However, specific representations only contain the unique information of each individual view, which limits their ability to fully excavate the diversity of multi-view data to enhance the complementarity among different views. Moreover, when conducting multi-view subspace clustering, the learned subspace self-representation and clustering are sequential and independent, which lacks consideration of the interaction between representation learning and the final clustering calculation. In this paper, a novel method termed consistent and diverse multi-view subspace clustering with structure constraint (CDMSC${}^2$) is proposed to overcome the above-described deficiencies. (1) An exclusivity constraint term is employed to enhance the diversity of specific representations among different views for modeling consistency and diversity in a unified framework. (2) A clustering structure constraint is imposed on the subspace self-representation by factorizing the learned subspace self-representation into the cluster centroids and the cluster assignments with the goal of obtaining a clustering-oriented subspace self-representation. In addition, we carefully designed an efficient optimization algorithm to solve the objective function through relaxation and alternating minimization. Extensive experiments on five benchmark datasets in terms of six evaluation metrics demonstrate that our method outperforms the state-of-the-art methods.

最近开发了多视图子空间聚类算法，通过准确描述多视图数据的基本特征来处理多视图数据集聚类。大多数现有方法都侧重于使用一致表示和一组具有精心设计的正则化的特定表示来学习不同视图之间的共同和特定知识，从而进行自我表示属性。然而，特定表示只包含每个单独视图的独特信息，这限制了它们充分挖掘多视图数据的多样性以增强不同视图之间的互补性的能力。而且，在进行多视图子空间聚类时，学习到的子空间自我表示和聚类是顺序独立的，缺乏对表征学习和最终聚类计算之间的相互作用的考虑。在本文中，一种称为具有结构约束的一致和多样的多视图子空间聚类（CDMSC${}^2$) 旨在克服上述缺陷。(1) 使用排他性约束项来增强不同视图之间特定表示的多样性，以在统一框架中建模一致性和多样性。(2) 通过将学习到的子空间自表示分解为聚类质心和聚类分配，对子空间自表示施加聚类结构约束，目的是获得面向聚类的子空间自表示。此外，我们精心设计了一种高效的优化算法，通过松弛和交替最小化来求解目标函数。在六个评估指标方面对五个基准数据集进行的大量实验表明，我们的方法优于最先进的方法。