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Convolutional Neural Networks on Graphs with Fast ...

Convolutional Neural Networks on Graphswith Fast Localized Spectral FilteringMicha l DefferrardXavier BressonPierre VandergheynstEPFL, Lausanne, this work, we are interested in generalizing Convolutional Neural Networks (CNNs) from low-dimensional regular grids, where image, video and speech arerepresented, to high-dimensional irregular domains, such as social Networks , brainconnectomes or words embedding, represented by Graphs . We present a formu-lation of CNNs in the context of spectral graph theory, which provides the nec-essary mathematical background and efficient numerical schemes to design fastlocalized Convolutional filters on Graphs .

Polynomial parametrization for localized filters. There are however two limitations with non-parametric filters: (i) they are not localized in space and (ii) their learning complexity is in O(n), the dimensionality of the data. These issues can be overcome with the use of a polynomial filter g () = KX 1 k=0 k k; (3)

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