Generalized Kuramoto Models & Hyperbolic Graph Clustering in Lorentz Space | HackerNoon

Table of Links

Abstract and 1. Introduction

2. Related Work

3. Preliminaries and Notations

4. Differentiable Structural Information

   4.1. A New Formulation

   4.2. Properties

   4.3. Differentiability & Deep Graph Clustering

5. LSEnet

   5.1. Embedding Leaf Nodes

   5.2. Learning Parent Nodes

   5.3. Hyperbolic Partitioning Tree

6. Experiments

   6.1. Graph Clustering

   6.2. Discussion on Structural Entropy

7. Conclusion, Broader Impact, and References Appendix

A. Proofs

B. Hyperbolic Space

C. Technical Details

D. Additional Results

3. Preliminaries and Notations

Herein, different from the typical setting of existing works, we are interested in a more challenging problem of graph clustering with unknown cluster number. Some preliminary concepts and notations are introduced here.

Throughout this paper, the lowercase boldfaced x and uppercase X denote vector and matrix, respectively. The notation table is given in Appendix C.1.

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Authors:

(1) Li Sun, North China Electric Power University, Beijing 102206, China ([email protected]);

(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.

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This paper is available on arxiv under CC BY-NC-SA 4.0 Deed (Attribution-Noncommercial-Sharelike 4.0 International) license.

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