Gaussian-Induced Convolution for Graphs
This work addresses the challenge of applying convolution to coordinate-free graphs, which is important for tasks like pattern recognition, but it appears incremental as it builds on existing graph convolution methods.
The paper tackles the problem of learning representations on irregular graphs by proposing a Gaussian-induced convolution framework that integrates edge information into Gaussian models for local convolution filtering, achieving state-of-the-art results on graph classification datasets.
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.