  Learning representation on graph plays a crucial role in numerous tasks of
pattern recognition. Different from grid-shaped images/videos, on which local
convolution kernels can be lattices, however, graphs are fully coordinate-free
on vertices and edges. In this work, we propose a Gaussian-induced convolution
(GIC) framework to conduct local convolution filtering on irregular graphs.
Specifically, an edge-induced Gaussian mixture model is designed to encode
variations of subgraph region by integrating edge information into weighted
Gaussian models, each of which implicitly characterizes one component of
subgraph variations. In order to coarsen a graph, we derive a vertex-induced
Gaussian mixture model to cluster vertices dynamically according to the
connection of edges, which is approximately equivalent to the weighted graph
cut. We conduct our multi-layer graph convolution network on several public
datasets of graph classification. The extensive experiments demonstrate that
our GIC is effective and can achieve the state-of-the-art results.
