Geometric Perspectives on Graph-based Learning Algorithms

This repository contains supplementary materials for the PhD thesis titled "Geometric Perspectives on Graph-based Learning Algorithms".

Summary

1. Dynamics of the accelerated t-SNE

   • The first part is based on the Dynamics of the accelerated t-SNE submitted to and reviewed by TMLR (official).
   • In addition to the reviewed content, this repository includes several extra experiments. The corresponding implementation and runnable scripts are placed under the Dynamics_of_the_accelerated_t-SNE, with experiment scripts mainly organized in Dynamics_of_the_accelerated_t-SNE/experiments.

2. Sobolev Ricci Curvature

   • The second part focuses on Sobolev Ricci Curvature, which extracts tree structures from graphs and is closely related to Ollivier Ricci Curvature. This work is available as a preprint at　Sobolev--Ricci Curvature
   • Implementation and experiment scripts are organized under the SobolevRicciCurvature. For application-oriented tasks, please check the two main artifacts:
     • SobolevRicciCurvature/community_detection
     • SobolevRicciCurvature/manl

Repository structure

Directory	Description
Dynamics_of_the_accelerated_t-SNE/	Code and notebooks for the accelerated t-SNE experiments, including GD/MM/NAG comparisons, ARR computation, and additional experiments for the dissertation.
Dynamics_of_the_accelerated_t-SNE/experiments/	Scripts for ARR-stopped continuous relaxations, comparison with discrete t-SNE, KL-divergence trajectories, and momentum sweep experiments.
SobolevRicciCurvature/community_detection/	Community-detection experiments using SRC/ORC, including SBM, LFR, real graph datasets, ablation studies, and cycle-controlled ORC--SRC discrepancy experiments.
SobolevRicciCurvature/manl/	MANL / edge-pruning experiments using ORC and SRC variants.

Reproducing dissertation experiments

The code is organized by dissertation topic.

• For Chapter 3, see Dynamics_of_the_accelerated_t-SNE/experiments/README_tsne.md. This includes ARR computation, ARR-stopped continuous relaxations, comparison with the original discrete t-SNE update, KL-divergence trajectories, and momentum-sweep experiments.
• For Chapter 4 community-detection experiments, see SobolevRicciCurvature/community_detection/README.md.
• For Chapter 4 MANL / edge-pruning experiments, see SobolevRicciCurvature/manl/README.md.

Citation

If you use this repository, please cite the corresponding dissertation or the related papers listed above. A formal citation will be added after the dissertation is published.