From Spectrum Wavelet to Vertex Propagation: Graph Convolutional Networks Based on Taylor Approximation
arXiv:2007.00730
Abstract
Graph convolutional networks (GCN) have been recently utilized to extract the underlying structures of datasets with some labeled data and high-dimensional features. Existing GCNs mostly rely on a first-order Chebyshev approximation of graph wavelet-kernels. Such a generic propagation model does not always suit the various datasets and their features. This work revisits the fundamentals of graph wavelet and explores the utility of signal propagation in the vertex domain to approximate the spectral wavelet-kernels. We first derive the conditions for representing the graph wavelet-kernels via vertex propagation. We next propose alternative propagation models for GCN layers based on Taylor expansions. We further analyze the choices of detailed graph representations for TGCNs. Experiments on citation networks, multimedia datasets and synthetic graphs demonstrate the advantage of Taylor-based GCN (TGCN) in the node classification problems over the traditional GCN methods.
References in corpus (15)
- The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
- Inductive Representation Learning on Large Graphs
- Geometric deep learning: going beyond Euclidean data
- Discrete Signal Processing on Graphs
- Discrete Signal Processing on Graphs: Sampling Theory
- Stationary signal processing on graphs
- Residual Gated Graph ConvNets
- Stationary Graph Processes and Spectral Estimation
- Topological Signal Processing over Simplicial Complexes
- Benchmarking Graph Neural Networks
- Fast Resampling of 3D Point Clouds via Graphs
- Geom-GCN: Geometric Graph Convolutional Networks
- Large-Scale 3D Shape Reconstruction and Segmentation from ShapeNet Core55
- Legendre expansion of the neutrino-antineutrino annihilation kernel: Influence of high order terms
- Graph Signal Processing: Modulation, Convolution, and Sampling