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：多视角聚类（MVC）基于非负矩阵因式分解（NMF）及其变体在最近几年受到了极大的关注，因为它们具有聚类可解释性的优势。然而，现有的基于NMF的多视角聚类方法分别在每个视图数据上执行NMF，并忽略了视图之间的影响。因此，它们不能很好地利用视图内部空间结构和视图之间的互补信息。为了解决这个问题，我们提出了半非负张量因式分解（Semi-NTF），并在具有单方面正交约束的Semi-NTF基础上发展了一种新的多视角聚类方法。我们的模型直接对由视图锚点图组成的第三阶张量进行Semi-NTF处理。因此，我们的模型直接考虑了视图之间的关系。此外，我们使用张量Schatten p-范数正则化作为第三阶张量的秩逼近，其表征了多视角数据的聚类结构并利用了视图之间的互补信息。此外，我们为所提出的方法提供了一种优化算法，并数学地证明了该算法总是收敛于KKT点。在各种基准数据集上进行的广泛实验表明，我们提出的方法能够达到满意的聚类性能。