Multi-view clustering (MVC) based on non-negative matrix factorization (NMF) and its variants have received a huge amount of attention in recent years due to their advantages in clustering interpretability. However, existing NMF-based multi-view clustering methods perform NMF on each view data respectively and ignore the impact of between-view. Thus, they can't well exploit the within-view spatial structure and between-view complementary information. To resolve this issue, we present semi-non-negative tensor factorization (Semi-NTF) and develop a novel multi-view clustering based on Semi-NTF with one-side orthogonal constraint. Our model directly performs Semi-NTF on the 3rd-order tensor which is composed of anchor graphs of views. Thus, our model directly considers the between-view relationship. Moreover, we use the tensor Schatten p-norm regularization as a rank approximation of the 3rd-order tensor which characterizes the cluster structure of multi-view data and exploits the between-view complementary information. In addition, we provide an optimization algorithm for the proposed method and prove mathematically that the algorithm always converges to the stationary KKT point. Extensive experiments on various benchmark datasets indicate that our proposed method is able to achieve satisfactory clustering performance.

翻译：近年来，基于非负矩阵分解（NMF）及其变体的多视图聚类（MVC）因在聚类可解释性方面的优势而备受关注。然而，现有基于NMF的多视图聚类方法分别对每个视图数据进行NMF分解，忽略了视图间的影响，导致无法充分利用视图内空间结构与视图间互补信息。为解决该问题，本文提出半非负张量分解（Semi-NTF）方法，并开发了一种基于Semi-NTF且带单侧正交约束的新型多视图聚类模型。该模型直接对由各视图锚点图构成的三阶张量执行Semi-NTF分解，从而直接建模视图间关系。此外，我们采用张量Schatten p-范数正则化作为三阶张量的秩近似，以表征多视图数据的聚类结构并挖掘视图间互补信息。同时，我们为该模型设计了优化算法，并从数学上证明该算法始终收敛于KKT稳定点。在多种基准数据集上的大量实验表明，所提方法能够实现令人满意的聚类性能。