Spectral Networks and Locally Connected Networks on Graphs
This work addresses the challenge of applying CNNs to graph-structured data, which is incremental as it builds on existing CNN concepts for new domains.
The paper tackles the problem of generalizing convolutional neural networks to signals on non-translational domains like graphs, proposing two constructions based on hierarchical clustering and graph Laplacian spectra, and shows that for low-dimensional graphs, convolutional layers can be learned with parameters independent of input size, enabling efficient deep architectures.
Convolutional Neural Networks are extremely efficient architectures in image and audio recognition tasks, thanks to their ability to exploit the local translational invariance of signal classes over their domain. In this paper we consider possible generalizations of CNNs to signals defined on more general domains without the action of a translation group. In particular, we propose two constructions, one based upon a hierarchical clustering of the domain, and another based on the spectrum of the graph Laplacian. We show through experiments that for low-dimensional graphs it is possible to learn convolutional layers with a number of parameters independent of the input size, resulting in efficient deep architectures.