Graph Coordinates and Conventional Neural Networks -- An Alternative for
  Graph Neural Networks
Zheyi Qin Randy Paffenroth Anura P. Jayasumana
Graph-based data present unique challenges and opportunities for machine
learning. Graph Neural Networks (GNNs), and especially those algorithms that
capture graph topology through message passing for neighborhood aggregation,
have been a leading solution. However, these networks often require substantial
computational resources and may not optimally leverage the information
contained in the graph's topology, particularly for large-scale or complex
graphs. We propose Topology Coordinate Neural Network (TCNN) and Directional
Virtual Coordinate Neural Network (DVCNN) as novel and efficient alternatives
to message passing GNNs, that directly leverage the graph's topology,
sidestepping the computational challenges presented by competing algorithms.
Our proposed methods can be viewed as a reprise of classic techniques for graph
embedding for neural network feature engineering, but they are novel in that
our embedding techniques leverage ideas in Graph Coordinates (GC) that are
lacking in current practice. Experimental results, benchmarked against the Open
Graph Benchmark Leaderboard, demonstrate that TCNN and DVCNN achieve
competitive or superior performance to message passing GNNs. For similar levels
of accuracy and ROC-AUC, TCNN and DVCNN need far fewer trainable parameters
than contenders of the OGBN Leaderboard. The proposed TCNN architecture
requires fewer parameters than any neural network method currently listed in
the OGBN Leaderboard for both OGBN-Proteins and OGBN-Products datasets.
Conversely, our methods achieve higher performance for a similar number of
trainable parameters. By providing an efficient and effective alternative to
message passing GNNs, our work expands the toolbox of techniques for
graph-based machine learning.