Abstract and 1. Introduction

  1. Related Work

  2. Preliminaries and Notations

  3. Differentiable Structural Information

    4.1. A New Formulation

    4.2. Properties

    4.3. Differentiability & Deep Graph Clustering

  4. LSEnet

    5.1. Embedding Leaf Nodes

    5.2. Learning Parent Nodes

    5.3. Hyperbolic Partitioning Tree

  5. Experiments

    6.1. Graph Clustering

    6.2. Discussion on Structural Entropy

  6. Conclusion, Broader Impact, and References Appendix

A. Proofs

B. Hyperbolic Space

C. Technical Details

D. Additional Results

4.1. A New Formulation

To bridge this gap, we present a new formulation of structural information with the level-wise assignment, which is shown to be equivalent to the classic formulation in Eq. (2).

Proof. Please refer to Appendix A.1.

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.