Interferometric Graph Transform: a Deep Unsupervised Graph Representation

TL;DR

The paper introduces the Interferometric Graph Transform, a novel deep unsupervised spectral graph neural network that effectively captures discriminative and invariant features, achieving state-of-the-art results across diverse graph-based tasks.

Contribution

It presents a generic complex-valued spectral graph architecture with a new greedy objective, enabling better topology exploitation and analytic operator recovery for vision and graph tasks.

Findings

Achieved state-of-the-art results in image classification, community detection, and action recognition.

Demonstrated the effectiveness of spectral domain topology exploitation.

Recovered analytic operators for vision tasks.

Abstract

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.