Function Space Pooling For Graph Convolutional Networks

Corcoran, Padraig Machine Learning 

Many real world data such as social networks, collections of documents and chemical structures are naturally represented as graphs. Consequently there exists great potential for the application of machine learning to graphs. Given the great successes of neural networks or deep learning to the analysis of images, there has recently been much research considering the application or generalization of neural networks to graphs. In many cases this has resulted in state of the art performance in many tasks (Wu et al., 2019). Graph convolutional is a neural network architecture commonly applied to graphs. This architecture consists of a sequence of convolutional layers where each layer iteratively updates a representation or embedding of each vertex. This update is achieved through the application of an operation which considers the current representation of each vertex plus the current representation of its adjacent neighbours (Gilmer et al., 2017). The output of a sequence of convolutional layers is a representation of each vertex which encodes properties of the vertex in question and vertices in its neighbourhood. If one wishes to perform a vertex centric task such as vertex classification, then one may operate directly on the set of vertex representations output from a sequence of convolutional layers.

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