Geometric deep learning -- Convolutional Neural Networks on Graphs and Manifolds

The main idea of spectral approaches such as Graph neural networks is to generalize the Fourier transform theorem for graph and manifold data and doing the convolution on the spectral domain. The generalization of the Fourier transform consists on using the already defined eigenfunctions of graph laplacian as bases for the Fourier transform. The process to apply a convolution using this generalization is as follows. This approach has presented very good results on data presented as a graph, but has an important weakness: Laplacian eigenfunctions are inconsistent across different domains.