602 research outputs found
CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters
The rise of graph-structured data such as social networks, regulatory
networks, citation graphs, and functional brain networks, in combination with
resounding success of deep learning in various applications, has brought the
interest in generalizing deep learning models to non-Euclidean domains. In this
paper, we introduce a new spectral domain convolutional architecture for deep
learning on graphs. The core ingredient of our model is a new class of
parametric rational complex functions (Cayley polynomials) allowing to
efficiently compute spectral filters on graphs that specialize on frequency
bands of interest. Our model generates rich spectral filters that are localized
in space, scales linearly with the size of the input data for
sparsely-connected graphs, and can handle different constructions of Laplacian
operators. Extensive experimental results show the superior performance of our
approach, in comparison to other spectral domain convolutional architectures,
on spectral image classification, community detection, vertex classification
and matrix completion tasks
LFGCN: Levitating over Graphs with Levy Flights
Due to high utility in many applications, from social networks to blockchain
to power grids, deep learning on non-Euclidean objects such as graphs and
manifolds, coined Geometric Deep Learning (GDL), continues to gain an ever
increasing interest. We propose a new L\'evy Flights Graph Convolutional
Networks (LFGCN) method for semi-supervised learning, which casts the L\'evy
Flights into random walks on graphs and, as a result, allows both to accurately
account for the intrinsic graph topology and to substantially improve
classification performance, especially for heterogeneous graphs. Furthermore,
we propose a new preferential P-DropEdge method based on the Girvan-Newman
argument. That is, in contrast to uniform removing of edges as in DropEdge,
following the Girvan-Newman algorithm, we detect network periphery structures
using information on edge betweenness and then remove edges according to their
betweenness centrality. Our experimental results on semi-supervised node
classification tasks demonstrate that the LFGCN coupled with P-DropEdge
accelerates the training task, increases stability and further improves
predictive accuracy of learned graph topology structure. Finally, in our case
studies we bring the machinery of LFGCN and other deep networks tools to
analysis of power grid networks - the area where the utility of GDL remains
untapped.Comment: To Appear in the 2020 IEEE International Conference on Data Mining
(ICDM
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