Almost all of the existing methods assume that the samples between different views have a strict one-to-one relationship whether it is for complete multi-view data or for partial multi-view data. In this paper, we refer to the neglected many-to-many relationship between cross-view samples as the complex mapping relationship between views. To address this issue, we propose a resultful Complex Mapping Multi-View Clustering (CMMVC) method by exploring the complex mapping relationship between views. We firstly construct a complex mapping relationship matrix for each pair of views by using the nearest neighbor relationship between cross-view samples. Then the complex mapping relationship matrix is introduced into the framework of multi-view clustering based on non-negative matrix factorization to guide multi-view information fusion in order to obtain more compact representation of multi-view data space. Finally, we give the objective function of CMMVC and an effective optimization scheme. The experimental results demonstrate the advantages of the proposed CMMVC method on multi-view clustering tasks by mining the complex mapping relationship between different views.

几乎所有现有方法都假定不同视图之间的样本具有严格的一对一关系，无论是用于完整的多视图数据还是用于部分多视图数据。在本文中，我们将交叉视图样本之间被忽略的多对多关系称为视图之间的复杂映射关系。为了解决此问题，我们通过探索视图之间的复杂映射关系，提出了一种有效的复杂映射多视图聚类（CMMVC）方法。首先，我们使用交叉视图样本之间的最近邻关系为每对视图构造一个复杂的映射关系矩阵。然后将复杂的映射关系矩阵引入基于非负矩阵分解的多视图聚类框架中，以指导多视图信息融合，以获得更紧凑的多视图数据空间表示。最后，给出了CMMVC的目标函数和有效的优化方案。实验结果通过挖掘不同视图之间的复杂映射关系，证明了所提出的CMMVC方法在多视图聚类任务中的优势。