Multi-view clustering aims at integrating the complementary information between different views so as to obtain an accurate clustering result. In addition, the traditional clustering is a kind of unsupervised learning method, which does not take the label information into learning. In this paper, we propose a novel model, called semi-supervised multi-view clustering based on orthonormality-constrained nonnegative matrix factorization (MVOCNMF), to cluster the multi-view data into a number of categories. In the proposed model, based on the label information, we first learn the low-dimensional representations of data by the constrained NMF technique, and simultaneously cluster the samples with the same label into the clustering prototypes for each view. After that, we put forward a novel orthonormality constraint term to obtain the desirable representations for each view, and use the co-regularization to integrate the complementary information from different views. We further develop an alternating minimization algorithm to solve the proposed model, and present the convergence analysis and computational complexity of the proposed method. Extensive experimental results on several multi-view datasets have shown that the proposed MVOCNMF method outperforms the existing multi-view clustering methods.

多视图聚类的目的是整合不同视图之间的互补信息，以获得准确的聚类结果。另外，传统的聚类是一种无监督的学习方法，它不会将标签信息带入学习中。在本文中，我们提出了一种基于正交正态约束的非负矩阵分解（MVOCNMF）的新型模型，称为半监督多视图聚类，将多视图数据聚类为多个类别。在提出的模型中，基于标签信息，我们首先通过约束NMF技术学习数据的低维表示，然后将具有相同标签的样本同时聚类到每个视图的聚类原型中。之后，我们提出了一个新的正交正态约束项，以获得每个视图的期望表示，并使用协正则化来整合来自不同视图的互补信息。我们进一步开发了一种交替最小化算法来求解所提出的模型，并提出了所提出方法的收敛性分析和计算复杂度。在多个多视图数据集上的大量实验结果表明，提出的MVOCNMF方法优于现有的多视图聚类方法。