Graph Convolutions and Machine Learning

Abstract

In recent years deep learning has produced significant improvements in the field of machine learning, with some of the greatest successes resulting from the application of convolutional neural networks to Euclidean data domains such as images and audio. Many modern data sets do not have such a simple structure, however, and are accordingly more difficult to process with standard machine learning techniques. This paper provides an introduction to deep learning applied to non-Euclidean data domains. Specifically,this paper considers the generalization of essential components of convolutional neural networks to data defined over graphs. The generalization of convolutional neural networks to non-Euclidean data sets such as graphs requires a convolution operator suitable for use over graphs. Such an operator is defined by analogy with the Fourier transform through the graph Laplacian matrix. These required elements are defined and the analogy between their Euclidean counterparts is developed. The explanation of the analogy is intended to be accessible to readers with relatively limited background in the subject areas involved. In addition to the theoretical material discussed,this paper considers certain computational concerns arising in practical applications of the theories presented, and summarizes a selection of existing applications of the techniques explored. The paper concludes with a discussion of an original extension of graph convolutional neural networks developed as a part of a research project in which the author participated.