Topological Node2vec: Improving Graph Embeddings with Persistent Homology

Explore the intersection of topology and machine learning in this 46-minute talk from the Applied Algebraic Topology Network. Delve into the theory, applications, and heuristics of incorporating topology into graph embeddings. Examine how persistent homology defines topology for point clouds and weighted graphs by analyzing pairwise distances and edge weights. Discover the challenges of preserving topology when transforming weighted edges into Euclidean distances using graph embedding methods. Learn about a novel topological loss term that addresses these issues, and gain insights into new developments in optimal transport as it relates to Topological Data Analysis (TDA). Enhance your understanding of graph embeddings and their topological implications through practical examples and theoretical discussions.