LSEnet: Lorentz Structural Entropy Neural Network for Deep Graph Clustering

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