Adaptive Graph Convolution Methods for Attributed Graph Clustering

Xiaotong Zhang, Han Liu, Qimai Li, Xiao-Ming Wu, Xianchao Zhang

Abstract: Attributed graph clustering is a challenging task as it requires to jointly model graph structure and node attributes. Although recent advances in graph convolutional networks have shown the effectiveness of graph convolution in combining structural and content information, there is limited understanding of how to properly apply it for attributed graph clustering. Previous methods commonly use a fixed and low order graph convolution, which only aggregates information of few-hop neighbours and hence cannot fully capture the cluster structures of diverse graphs. In this paper, we first propose an adaptive graph convolution method (AGC) for attributed graph clustering, which exploits high-order graph convolutions to capture global cluster structures and adaptively selects an appropriate order <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> via intra-cluster distance. While AGC can find a reasonable <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> and avoid over-smoothing, it is not sensitive to the gradual decline of clustering performance as <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> increases. To search for a better <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> , we further propose an improved adaptive graph convolution method (IAGC) that not only observes the variation of intra-cluster distance, but also considers the inconsistencies of filtered features with graph structure and raw features, respectively. We establish the validity of our methods by theoretical analysis and extensive experiments on various benchmark datasets.