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The rise of graph-structured data such as social networks, regulatorynetworks, citation graphs, and functional brain networks, in combination withresounding success of deep learning in various applications, has brought theinterest in generalizing deep learning models to non-Euclidean domains. In thispaper, we introduce a new spectral domain convolutional architecture for deeplearning on graphs. The core ingredient of our model is a new class ofparametric rational complex functions (Cayley polynomials) allowing toefficiently compute spectral filters on graphs that specialize on frequencybands of interest. Our model generates rich spectral filters that are localizedin space, scales linearly with the size of the input data forsparsely-connected graphs, and can handle different constructions of Laplacianoperators. Extensive experimental results show the superior performance of ourapproach, in comparison to other spectral domain convolutional architectures,on spectral image classification, community detection, vertex classificationand matrix completion tasks.

CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters