  We propose the Interferometric Graph Transform (IGT), which is a new class of
deep unsupervised graph convolutional neural network for building graph
representations. Our first contribution is to propose a generic, complex-valued
spectral graph architecture obtained from a generalization of the Euclidean
Fourier transform. We show that our learned representation consists of both
discriminative and invariant features, thanks to a novel greedy concave
objective. From our experiments, we conclude that our learning procedure
exploits the topology of the spectral domain, which is normally a flaw of
spectral methods, and in particular our method can recover an analytic operator
for vision tasks. We test our algorithm on various and challenging tasks such
as image classification (MNIST, CIFAR-10), community detection (Authorship,
Facebook graph) and action recognition from 3D skeletons videos (SBU, NTU),
exhibiting a new state-of-the-art in spectral graph unsupervised settings.
