Upper Bounding Barlow Twins: A Novel Filter for Multi-Relational
  Clustering
Xiaowei Qian Bingheng Li Zhao Kang
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.