Stanford CS224W: Machine Learning with Graphs | 2021 | Lecture 19.2 - Hyperbolic Graph Embeddings

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Jure Leskovec
Computer Science, PhD

In previous lectures, we focused on graph representation learning in Euclidean embedding spaces. In this lecture, we introduce hyperbolic embedding spaces, which are great for modeling hierarchical, tree-like graphs. Moreover, we introduce basics for hyperbolic geometry models, which leads to the idea of hyperbolic GNNs. More details can be found in the paper: Hyperbolic Graph Convolutional Neural Networks: https://arxiv.org/abs/1910.12933

To follow along with the course schedule and syllabus, visit:
http://web.stanford.edu/class/cs224w/

0:00 Introduction
0:19 Hyperbolic Graph Embeddings
2:08 Graph Embedding Geometry
3:04 Hyperbolic Embedding Space
3:50 Hyperbolic Space Model (2)
10:32 Task
12:50 Hyperbolic Geometry (2)
15:20 Hyperbolic Geometry Models
18:12 Geodesic Distance (2)
20:26 Mapping to and from Tangent Space
22:31 Hyperbolic GNN (3)
31:03 Hyperbolic GNN: Summary

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