Graph clustering is a fundamental problem in machine learning. Deep learning
methods achieve the state-of-the-art results in recent years, but they still
cannot work without predefined cluster numbers. Such limitation motivates us to
pose a more challenging problem of graph clustering with unknown cluster
number. We propose to address this problem from a fresh perspective of graph
information theory (i.e., structural information). In the literature,
structural information has not yet been introduced to deep clustering, and its
classic definition falls short of discrete formulation and modeling node
features. In this work, we first formulate a differentiable structural
information (DSI) in the continuous realm, accompanied by several theoretical
results. By minimizing DSI, we construct the optimal partitioning tree where
densely connected nodes in the graph tend to have the same assignment,
revealing the cluster structure. DSI is also theoretically presented as a new
graph clustering objective, not requiring the predefined cluster number.
Furthermore, we design a neural LSEnet in the Lorentz model of hyperbolic
space, where we integrate node features to structural information via
manifold-valued graph convolution. Extensive empirical results on real graphs
show the superiority of our approach.

图聚类是机器学习中的一个基本问题，本文提出了一种使用图信息理论解决未知聚类数量的图聚类问题的方法，通过最小化可微分的结构信息，构建最优的分区树，其中稠密连接的节点在图中有相同的分配，并且在 Lorentz 模型中设计了神经 LSEnet 将节点特征与结构信息集成，实验证明该方法具有优越性。