Multi-view subspace clustering methods have employed learned self-representation tensors from different tensor decompositions to exploit low rank information. However, the data structures embedded with self-representation tensors may vary in different multi-view datasets. Therefore, a pre-defined tensor decomposition may not fully exploit low rank information for a certain dataset, resulting in sub-optimal multi-view clustering performance. To alleviate the aforementioned limitations, we propose the adaptively topological tensor network (ATTN) by determining the edge ranks from the structural information of the self-representation tensor, and it can give a better tensor representation with the data-driven strategy. Specifically, in multi-view tensor clustering, we analyze the higher-order correlations among different modes of a self-representation tensor, and prune the links of the weakly correlated ones from a fully connected tensor network. Therefore, the newly obtained tensor networks can efficiently explore the essential clustering information with self-representation with different tensor structures for various datasets. A greedy adaptive rank-increasing strategy is further applied to improve the capture capacity of low rank structure. We apply ATTN on multi-view subspace clustering and utilize the alternating direction method of multipliers to solve it. Experimental results show that multi-view subspace clustering based on ATTN outperforms the counterparts on six multi-view datasets.

翻译：多视角子空间聚类方法已采用从不同张量分解中学习到的自表示张量来挖掘低秩信息。然而，不同多视角数据集中嵌入自表示张量的数据结构可能有所差异。因此，针对特定数据集，预定义的张量分解可能无法充分挖掘低秩信息，导致多视角聚类性能欠佳。为缓解上述局限，我们提出自适应拓扑张量网络（ATTN），通过从自表示张量的结构信息中确定边缘秩，并借助数据驱动策略获得更优的张量表示。具体而言，在多视角张量聚类中，我们分析自表示张量不同模态间的高阶相关性，并从全连接张量网络中剪除弱相关模态的链接。由此获得的新张量网络能够针对不同数据集，通过不同张量结构高效探索自表示中的关键聚类信息。进一步采用贪婪自适应增秩策略以提升低秩结构的捕获能力。我们将ATTN应用于多视角子空间聚类，并采用交替方向乘子法进行求解。实验结果表明，基于ATTN的多视角子空间聚类在六个多视角数据集上均优于对比方法。