Explore topological data analysis in graph representation learning through this 57-minute lecture by Bastian Rieck. Delve into graph classification tasks using machine learning techniques, with a focus on incorporating topological features. Discover a novel 'topology-aware' layer for graph neural networks and its impact on theoretical expressivity. Gain insights into persistent homology, multifiltration learning, and experimental results on synthetic datasets. Suitable for TDA enthusiasts, with helpful but not required prior knowledge of machine learning techniques.
Overview
Syllabus
Introduction
Representation of graphs
Graph similarity analysis
Modern graph neural networks
Status quo
Topological features
Persistent homology
The choice of filtration
Graph Neural Networks
Multifiltration Learning
Theoretical Nuggets
Nonisomorphic Graphs
Experiments
Synthetic Data Sets
WL Test
Results
Removing node attributes
Comparing results
Taught by
Applied Algebraic Topology Network
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