Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Abstract and 1. Introduction Related Work


Preliminaries and Notations


Differentiable Structural Information
4.1. A New Formulation
4.2. Properties
4.3. Differentiability & Deep Graph Clustering


LSEnet
5.1. Embedding Leaf Nodes
5.2. Learning Parent Nodes
5.3. Hyperbolic Partitioning Tree


Experiments
6.1. Graph Clustering
6.2. Discussion on Structural Entropy


Conclusion, Broader Impact, and References Appendix Related Work Related Work Related Work Related Work Preliminaries and Notations Preliminaries and Notations Preliminaries and Notations Preliminaries and Notations Differentiable Structural Information
4.1. A New Formulation
4.2. Properties
4.3. Differentiability & Deep Graph Clustering Differentiable Structural Information Differentiable Structural Information Differentiable Structural Information 4.1. A New Formulation 4.1. A New Formulation 4.2. Properties 4.2. Properties 4.3. Differentiability & Deep Graph Clustering 4.3. Differentiability & Deep Graph Clustering LSEnet
5.1. Embedding Leaf Nodes
5.2. Learning Parent Nodes
5.3. Hyperbolic Partitioning Tree LSEnet LSEnet LSEnet 5.1. Embedding Leaf Nodes 5.1. Embedding Leaf Nodes 5.2. Learning Parent Nodes 5.2. Learning Parent Nodes 5.3. Hyperbolic Partitioning Tree 5.3. Hyperbolic Partitioning Tree Experiments
6.1. Graph Clustering
6.2. Discussion on Structural Entropy Experiments Experiments 6.1. Graph Clustering 6.1. Graph Clustering 6.2. Discussion on Structural Entropy 6.2. Discussion on Structural Entropy Conclusion, Broader Impact, and References Appendix Conclusion, Broader Impact, and References Appendix Conclusion, Broader Impact, and References Appendix Conclusion, Broader Impact, and References Appendix A. Proofs A. Proofs B. Hyperbolic Space B. Hyperbolic Space C. Technical Details C. Technical Details D. Additional Results D. Additional Results 7. Conclusion In this paper, we study graph clustering without predefined cluster number from a new perspective of structural entropy. We formulate a new graph clustering objective (DSI) not requiring the cluster number, so that the clusters are revealed in the optimal partitioning tree given by DSI minimization. Furthermore, we present a neural LSEnet to learn the optimal tree in hyperbolic space, where we integrate node features to structural information with Lorentz graph convolution net. Extensive empirical results show the superiority of our approach on real graphs. Broader Impact This paper presents work whose goal is to bridge the structural entropy of information theory and deep learning and shows a new objective function for deep graph clustering, not requiring the predefined cluster number. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here. References Almahairi, A., Ballas, N., Cooijmans, T., Zheng, Y., Larochelle, H., and Courville, A. Dynamic capacity networks. In Proceedings of the ICML, pp. 2549–2558. PMLR, 2016. Bachmann, G., Becigneul, G., and Ganea, O. Constant cur- ´ vature graph convolutional networks. In Proceedings of the 37th International Conference on Machine Learning (ICML), volume 119, pp. 486–496. 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In Proceedings of the Web Conference 2021, pp. 1249–1261. ACM / IW3C2, 2021. Zou, D., Peng, H., Huang, X., Yang, R., Li, J., Wu, J., Liu, C., and Yu, P. S. Se-gsl: A general and effective graph structure learning framework through structural entropy optimization. In Proceedings of the ACM Web Conference, pp. 499–510, 2023. Authors:
(1) Li Sun, North China Electric Power University, Beijing 102206, China (ccesunli@ncepu.edu);
(2) Zhenhao Huang, North China Electric Power University, Beijing 102206, China;
(3) Hao Peng, Beihang University, Beijing 100191, China;
(4) Yujie Wang, North China Electric Power University, Beijing 102206, China;
(5) Chunyang Liu, Didi Chuxing, Beijing, China;
(6) Philip S. Yu, University of Illinois at Chicago, IL, USA. Authors: Authors: (1) Li Sun, North China Electric Power University, Beijing 102206, China (ccesunli@ncepu.edu); (2) Zhenhao Huang, North China Electric Power University, Beijing 102206, China; (3) Hao Peng, Beihang University, Beijing 100191, China; (4) Yujie Wang, North China Electric Power University, Beijing 102206, China; (5) Chunyang Liu, Didi Chuxing, Beijing, China; (6) Philip S. Yu, University of Illinois at Chicago, IL, USA. This paper is available on arxiv under CC BY-NC-SA 4.0 Deed (Attribution-Noncommercial-Sharelike 4.0 International) license. This paper is available on arxiv under CC BY-NC-SA 4.0 Deed (Attribution-Noncommercial-Sharelike 4.0 International) license. available on arxiv available on arxiv

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Automatic Data Grouping: LSEnet and the Future of Self-Organizing Networks

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