Multi-view clustering has been deeply explored since the compatible and complementary information among views can be well captured. Recently, the low-rank tensor representation-based methods have effectively improved the clustering performance by exploring high-order correlations between multiple views. However, most of them often express the low-rank structure of the self-representative tensor by the sum of unfolded matrix nuclear norms, which may cause the loss of information in the tensor structure. In addition, the amount of effective information in all views is not consistent, and it is unreasonable to treat their contribution to clustering equally. To address the above issues, we propose a novel weighted low-rank tensor representation (WLRTR) method for multi-view subspace clustering, which encodes the low-rank structure of the representation tensor through Tucker decomposition and weights the core tensor to retain the main information of the views. Under the augmented Lagrangian method framework, an iterative algorithm is designed to solve the WLRTR method. Numerical studies on four real databases have proved that WLRTR is superior to eight state-of-the-art clustering methods.

由于可以很好地捕获视图之间的兼容和互补信息，因此对多视图聚类进行了深入研究。最近，基于低秩张量表示的方法通过探索多个视图之间的高阶相关性，有效地改善了聚类性能。但是，它们中的大多数经常通过未展开的矩阵核规范的总和来表示自表示张量的低秩结构，这可能会导致张量结构中的信息丢失。此外，所有视图中有效信息的数量并不一致，并且将它们对聚类的贡献同等对待是不合理的。为了解决上述问题，我们提出了一种新颖的加权低秩张量表示（WLRTR）方法，用于多视图子空间聚类，它通过塔克（Tucker）分解对表示张量的低阶结构进行编码，并对核心张量加权，以保留视图的主要信息。在增强拉格朗日方法框架下，设计了一种迭代算法来求解WLRTR方法。对四个真实数据库的数值研究证明，WLRTR优于八种最新的聚类方法。