Modularity aided consistent attributed graph clustering via coarsening

TMLR Paper3038 Authors

Abstract: Graph clustering is an important unsupervised learning technique for partitioning graphs with attributes and detecting communities. However, current methods struggle to accurately capture true community structures and intra-cluster relations, be computationally efficient, and identify smaller communities. We address these challenges by integrating coarsening and modularity maximization, effectively leveraging both adjacency and node features to enhance clustering accuracy. We propose a loss function incorporating log-determinant, smoothness, and modularity components using a block majorization-minimization technique, resulting in superior clustering outcomes. The method is theoretically consistent under the Degree-Corrected Stochastic Block Model (DC-SBM), ensuring asymptotic error-free performance and complete label recovery. Our provably convergent and time-efficient algorithm seamlessly integrates with Graph Neural Networks (GNNs) and Variational Graph AutoEncoders (VGAEs) to learn enhanced node features and deliver exceptional clustering performance. Extensive experiments on benchmark datasets demonstrate its superiority over existing state-of-the-art methods for both attributed and non-attributed graphs.

Submission Length: Regular submission (no more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=wvySSGOLzf

Changes Since Last Submission:

We have made the following changes which incorporate Reviewer BtxT's feedback:
- Clarified the first reference of Q-MAGC.
- Defined the soft and hard versions of the cluster assignment matrix C more clearly.
- Corrected grammatical errors.
- Added the reason behind using DC-SBM in Appendix I.

Here is the [PDF diff (anonymized link)](https://anonymous.4open.science/api/repo/MAGC-8880/file/diffchecker%20rebuttal.pdf?v=afcb6801) for convenience.\
On the left side is the old version, and on the right side is the new version.\
Text in red is removed, in green is added and in blue is just moved without edits.

Assigned Action Editor: ~Seungjin_Choi1

Submission Number: 3038