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 5.2. Learning Parent Nodes A primary challenge is that, in the partitioning tree, the node number at each internal level is unknown. To address this issue, we introduce a simple yet effective method, setting a large enough node number Nh at the h-th level. A large Nh may introduce redundant nodes and result in a relaxed partitioning tree. According to Theorem 4.8 established in Sec. 4.3, redundant nodes in the partitioning tree do not affect the value of structural entropy, and finally present as empty leaf nodes by optimizing our objective. Theoretically, if an internal level has insufficient nodes, the self-organization of the graph can still be described by multiple levels in the partitioning tree. Theorem Remark. In fact, the geometric centroid in Theorem 5.2 is also equivalent to the gyro-midpoint in Poincare ball model ´ of hyperbolic space, detailed in Appendix B.4. Remark 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

Part of HackerNoon's growing list of open-source research papers, promoting free access to academic material.

Flexible Hierarchy Learning: Managing Unknown Node Counts in Curved Space

About Author

Comments

TOPICS

THIS ARTICLE WAS FEATURED IN

Related Stories

A Comparative Performance Analysis of SymTax on Five Citation Recommendation Datasets

It Is Okay If You Don't Know What You Like. We Do (feat. Deep Recommendation Algorithms)

10 Machine Learning, Data Science, and Deep Learning Courses for Programmers in 2020

10 Computer Vision Startups on Product Hunt with the Most Upvotes

10 Best Entry Level Machine Learning Tutorials

10 Best + Free Machine Learning Courses Collection

A Comparative Performance Analysis of SymTax on Five Citation Recommendation Datasets

It Is Okay If You Don't Know What You Like. We Do (feat. Deep Recommendation Algorithms)

10 Machine Learning, Data Science, and Deep Learning Courses for Programmers in 2020

10 Computer Vision Startups on Product Hunt with the Most Upvotes

10 Best Entry Level Machine Learning Tutorials

10 Best + Free Machine Learning Courses Collection

Light-Mode

Classic

Newspaper

Minty

Dark-Mode

Neon Noir

Minty

HN StartUps