Graph Based Convolutional Neural Network

In this paper we present a method for the application of Convolutional Neural Network (CNN) operators for use in domains which exhibit irregular spatial geometry by use of the spectral domain of a graph Laplacian, Figure 1. This allows learning of localized features in irregular domains by defining neighborhood relationships as edge weights between vertices in graph G. By formulating the domain as a fixed graph representation and projecting the observed data onto G as a graph signal f we are able to utilize the convolution theorem via a graph Fourier transform, matrix multiplication with the columnwise eigenvector matrix U , and elementwise multiplication with spectral filters k to learn feature maps (1).