Week 05 — Spectral Graph Learning

Convolution on graphs via the graph Laplacian. Why ChebNet matters and why most modern GNNs went back to spatial methods.

Lecture

The graph Laplacian and its spectrum · spectral filters · ChebNet (Defferrard 2016) · GCN (Kipf-Welling 2017) as a degenerate ChebNet · spectral methods on signed and directed graphs.

Read before the lecture

• Defferrard, Bresson, Vandergheynst, *Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering* (NeurIPS 2016)

Recitation — paper discussion

Kipf, Welling, *Semi-Supervised Classification with Graph Convolutional Networks* (ICLR 2017) (paper)

Come ready to argue one side of each:

• Is GCN really a spectral method or a spatial one in disguise?
• What does the simplification cost in terms of expressive power?

Reference text for this week: chapter 05 of the bilingual notes — EN PDF · FR PDF.