Simplifying Clustering with Graph Neural Networks
DOI:
https://doi.org/10.7557/18.6790Keywords:
Graph Neural Networks, Graph Clustering, Spectral ClusteringAbstract
The objective functions used in spectral clustering are generally composed of two terms: i) a term that minimizes the local quadratic variation of the cluster assignments on the graph and; ii) a term that balances the clustering partition and helps avoiding degenerate solutions.
This paper shows that a graph neural network, equipped with suitable message passing layers, can generate good cluster assignments by optimizing only a balancing term.
Results on attributed graph datasets show the effectiveness of the proposed approach in terms of clustering performance and computation time.
References
F. M. Bianchi, D. Grattarola, and C. Alippi. Spectral clustering with graph neural networks for graph pooling. In International Conference on Machine Learning, pages 874–883. PMLR, 2020.
M. Defferrard, X. Bresson, and P. Vandergheynst. Convolutional neural networks on graphs with fast localized spectral filtering. Advances in neural information processing systems, 29, 2016.
J. Gilmer, S. S. Schoenholz, P. F. Riley, O. Vinyals, and G. E. Dahl. Neural message passing for quantum chemistry. In International conference on machine learning. PMLR, 2017.
D. Grattarola, D. Zambon, F. M. Bianchi, and C. Alippi. Understanding pooling in graph neural networks. IEEE Transactions on Neural Networks and Learning Systems, 2022.
A. Grover and J. Leskovec. node2vec: Scalable feature learning for networks. In Proceedings of the 22nd ACM SIGKDD international conference on Knowledge discovery and data mining, 2016.
W. L. Hamilton. Graph representation learning. Synthesis Lectures on Artificial Intelligence and Machine Learning, 14(3):1–159, 2020.
M. Hein and S. Setzer. Beyond spectral clustering-tight relaxations of balanced graph cuts. In NIPS. Citeseer, 2011.
M. Kampffmeyer, S. Løkse, F. M. Bianchi, L. Livi, A.-B. Salberg, and R. Jenssen. Deep divergence-based approach to clustering. Neural Networks, 113:91–101, 2019.
T. N. Kipf and M. Welling. Semi-supervised classification with graph convolutional networks. International Conference on Learning Representations, 2016.
T. N. Kipf and M. Welling. Variational graph auto-encoders. arXiv preprint arXiv:1611.07308, 2016.
B. Perozzi, R. Al-Rfou, and S. Skiena. Deepwalk: Online learning of social representations. In Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining, 2014.
J. Qiu, Y. Dong, H. Ma, J. Li, K. Wang, and J. Tang. Network embedding as matrix factorization: Unifying deepwalk, line, pte, and node2vec. In Proceedings of the 11th ACM in ternational conference on web search and data mining, 2018.
A. Tsitsulin, J. Palowitch, B. Perozzi, and E. M ̈uller. Graph clustering with graph neural networks. arXiv preprint arXiv:2006.16904, 2020.
U. Von Luxburg. A tutorial on spectral clustering. Statistics and computing, 17(4):395–416, 2007.
Z. Ying, J. You, C. Morris, X. Ren, W. Hamilton, and J. Leskovec. Hierarchical graph representation learning with differentiable pooling. Advances in neural information processing systems, 31, 2018.
S. Zhou, H. Xu, Z. Zheng, J. Chen, J. Bu, J. Wu, X. Wang, W. Zhu, M. Ester, et al. A comprehensive survey on deep clustering: Taxonomy, challenges, and future directions. arXiv preprint arXiv:2206.07579, 2022.
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Copyright (c) 2023 Filippo Maria Bianchi
This work is licensed under a Creative Commons Attribution 4.0 International License.