Graph clustering is a longstanding research topic, and has achieved remarkable success with the deep learning methods in recent years. Nevertheless, we observe that several important issues largely remain open. On the one hand, graph clustering from the geometric perspective is appealing but has rarely been touched before, as it lacks a promising space for geometric clustering. On the other hand, contrastive learning boosts the deep graph clustering but usually struggles in either graph augmentation or hard sample mining. To bridge this gap, we rethink the problem of graph clustering from geometric perspective and, to the best of our knowledge, make the first attempt to introduce a heterogeneous curvature space to graph clustering problem. Correspondingly, we present a novel end-to-end contrastive graph clustering model named CONGREGATE, addressing geometric graph clustering with Ricci curvatures. To support geometric clustering, we construct a theoretically grounded Heterogeneous Curvature Space where deep representations are generated via the product of the proposed fully Riemannian graph convolutional nets. Thereafter, we train the graph clusters by an augmentation-free reweighted contrastive approach where we pay more attention to both hard negatives and hard positives in our curvature space. Empirical results on real-world graphs show that our model outperforms the state-of-the-art competitors.

翻译：图聚类是一个长期的研究课题，近年来深度学习方法取得了显著成功。然而，我们观察到几个重要问题仍然很大程度上未解决。一方面，从几何角度进行图聚类具有吸引力，但此前鲜有涉及，因缺乏适合几何聚类的理想空间。另一方面，对比学习推动了深度图聚类的发展，但通常在图增强或困难样本挖掘方面面临挑战。为弥补这一空白，我们从几何视角重新思考图聚类问题，并据我们所知，首次尝试将异质曲率空间引入图聚类问题。相应地，我们提出了一种名为CONGREGATE的端到端对比图聚类模型，利用里奇曲率解决几何图聚类。为支持几何聚类，我们构建了一个具有理论基础的异质曲率空间，通过所提出的全黎曼图卷积网络的乘积生成深度表示。在此基础上，我们采用一种无增强的重加权对比方法训练图聚类，在曲率空间中对困难负样本和困难正样本均给予更多关注。在真实世界图上的实验结果表明，我们的模型优于现有最先进的方法。