Matching Convolutional Neural Networks without Priors about Data

Convolutional Neural Networks (CNNs) [1] have been able to surpass traditional machine learning methods in various image based tasks [2], [3]. This is possible as they exploit the learning capabilities of deep neural networks while also taking advantage of the intrinsic regular 2D structure of the data. But when data lacks regular structure [4], there is no natural notion of convolutions, stride/pooling or data augmentation. Such irregularities occur in various domains covering social networks to neuroscience, internet of things, citation graphs, point cloud manifolds... The question of developing solutions that are counterparts of CNNs in irregular domains has recently been a very active field of research. In this paper we introduce a method that extends CNNs to irregular domains. Contrary to many alternative works, we ensure that our proposed methodology matches the performance of CNNs when applied to regular domains, even without knowledge of the underlying structure. To that end, we infer a graph to represent the topology of the data.