[Paper Review] Attributed Graph Clustering via Adaptive Graph Convolution

Xiaotong Zhang, Han Liu+2 more|arXiv (Cornell University)|Jun 4, 2019

Advanced Graph Neural Networks24 references24 citations

TL;DR

This paper proposes Adaptive Graph Convolution (AGC), a novel attributed graph clustering method that uses high-order graph convolution to capture global cluster structures and adaptively selects the optimal convolution order $k$ based on intra-cluster distance. AGC outperforms state-of-the-art methods by effectively integrating node features and graph structure, achieving superior clustering accuracy on benchmark datasets with minimal hyperparameter tuning.

ABSTRACT

Attributed graph clustering is challenging as it requires joint modelling of graph structures and node attributes. Recent progress on graph convolutional networks has proved that graph convolution is effective in combining structural and content information, and several recent methods based on it have achieved promising clustering performance on some real attributed networks. However, there is limited understanding of how graph convolution affects clustering performance and how to properly use it to optimize performance for different graphs. Existing methods essentially use graph convolution of a fixed and low order that only takes into account neighbours within a few hops of each node, which underutilizes node relations and ignores the diversity of graphs. In this paper, we propose an adaptive graph convolution method for attributed graph clustering that exploits high-order graph convolution to capture global cluster structure and adaptively selects the appropriate order for different graphs. We establish the validity of our method by theoretical analysis and extensive experiments on benchmark datasets. Empirical results show that our method compares favourably with state-of-the-art methods.

Motivation & Objective

• To address the limitation of fixed-order graph convolution in existing GCN-based methods, which often fail to capture global cluster structures in large or sparse attributed graphs.
• To develop a method that adaptively selects the optimal convolution order $k$ for different graph types, improving clustering performance across diverse network topologies.
• To enable effective joint modeling of node attributes and graph structure without requiring deep neural network training, enhancing efficiency and stability.
• To establish a theoretically grounded criterion for $k$ selection that prevents over-smoothing and ensures high-quality feature representations for clustering.

Proposed method

• Proposes a $k$-order graph convolution as a low-pass filter to smooth node features, capturing long-range dependencies beyond immediate neighbors.
• Introduces an adaptive $k$ selection strategy based on the intra-cluster distance $d_{\text{intra}}(k)$, where $k$ is chosen such that $d_{\text{intra}}(k-1) > 0$ to avoid over-smoothing.
• Applies spectral clustering on the smoothed features to obtain final node cluster assignments, decoupling feature learning from clustering.
• Uses a non-trainable, analytical formulation for graph convolution, avoiding deep neural network training and reducing computational cost.
• Employs a validation criterion that ensures the selected $k$ corresponds to a stable and high-quality cluster partition.
• Designs the method to be scalable and efficient, with runtime independent of model depth and dependent only on $k$ and graph size.

Experimental results

Research questions

• RQ1 How does high-order graph convolution improve clustering performance compared to fixed-order GCN layers?
• RQ2 Can an adaptive selection of the convolution order $k$ lead to better clustering results across diverse attributed graph structures?
• RQ3 Does the proposed intra-cluster distance criterion $d_{\text{intra}}(k-1) > 0$ reliably identify optimal $k$ values that prevent over-smoothing?
• RQ4 How does AGC compare in performance and efficiency to state-of-the-art GCN-based attributed clustering methods like GAE, MGAE, and ARGE?
• RQ5 To what extent does AGC generalize across different types of attributed graphs, including sparse citation networks and dense web page networks?

Key findings

• AGC consistently outperforms both feature-only and structure-only clustering baselines by a large margin, demonstrating the benefit of joint modeling of attributes and structure.
• On Cora, Citeseer, and Pubmed, AGC significantly outperforms MGAE, the strongest baseline, with improvements in accuracy (up to 4.5 percentage points) and normalized mutual information.
• The selected $k$ values (12, 55, 60, 8 for Cora, Citeseer, Pubmed, Wiki) closely match the optimal $k$ in the range [0,60], validating the effectiveness of the adaptive selection criterion.
• AGC achieves high stability, with standard deviations of accuracy, NMI, and F1 below 1% across all datasets, indicating robustness.
• Despite using higher-order convolutions, AGC is more efficient than training-based methods like ARGE and ARVGE, with faster inference times on larger graphs like Pubmed.
• The method avoids over-smoothing, as evidenced by declining performance when $d_{\text{intra}}(k) \leq 0$, confirming the validity of the selection criterion.