Multi-relational clustering is a challenging task due to the fact that diverse semantic information conveyed in multi-layer graphs is difficult to extract and fuse. Recent methods integrate topology structure and node attribute information through graph filtering. However, they often use a low-pass filter without fully considering the correlation among multiple graphs. To overcome this drawback, we propose to learn a graph filter motivated by the theoretical analysis of Barlow Twins. We find that input with a negative semi-definite inner product provides a lower bound for Barlow Twins loss, which prevents it from reaching a better solution. We thus learn a filter that yields an upper bound for Barlow Twins. Afterward, we design a simple clustering architecture and demonstrate its state-of-the-art performance on four benchmark datasets.

翻译：多关系聚类是一项具有挑战性的任务，因为多层图中传达的多样语义信息难以提取和融合。现有方法通过图滤波器整合拓扑结构与节点属性信息，但通常仅使用低通滤波器，未能充分考虑多个图之间的相关性。为克服这一缺陷，我们受巴洛双胞胎理论分析启发，提出学习一种图滤波器。我们发现，具有负半定内积的输入为巴洛双胞胎损失提供了下界，这阻碍了其达到更优解。因此，我们学习一种能够为巴洛双胞胎产生上界的滤波器。随后，我们设计了一个简洁的聚类架构，并在四个基准数据集上展示了其最先进的性能。