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 localized regular filters on graphs that specialize onfrequency bands of interest. Our model scales linearly with the size of theinput data for sparsely-connected graphs, can handle different constructions ofLaplacian operators, and typically requires less parameters than previousmodels. Extensive experimental results show the superior performance of ourapproach on various graph learning problems.
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