LSEnet: Lorentz Structural Entropy Neural Network for Deep Graph Clustering
arxiv(2024)
摘要
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.
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