LSEnet: Mastering Automated Data Grouping in Curved Hyperbolic 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

5. LSEnet

We propose a novel Lorentz Structural Entropy neural Net (LSEnet), which aims to learn the optimal partitioning tree T ∗ net in the Lorentz model of hyperbolic space, where we further incorporate node features with structural information by graph convolution net. First, we show the reason we opt for hyperbolic space, rather than Euclidean space.

Hyperbolic space is well suited to embed the partitioning tree, and Theorem 5.1 does not hold for Euclidean space.

Overall architecture of LSEnet is sketched in Figure 2. In hyperbolic space, LSEnet first embeds leaf nodes of the tree, and then recursively learns parent nodes, self-supervised by our new clustering objective Eq. (4).

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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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