Graph-based data present
unique challenges in machine learning, and while Graph
Neural Networks (GNNs) using message passing have been
effective, they often demand substantial computational
resources and may not fully leverage graph topology in large
or complex graphs. We introduce the Topology Coordinate
Neural Network (TCNN) and Directional Virtual Coordinate
Neural Network (DVCNN) as efficient alternatives that
directly utilize graph topology, bypassing the computational
demands of message passing. By revisiting classic graph
embedding techniques and incorporating novel Graph
Coordinates (GC), our methods address gaps in current
practices. Benchmarks against the Open Graph Benchmark
Leaderboard, TCNN and DVCNN demonstrate competitive or
superior performance compared to message passing GNNs using
significantly fewer trainable parameters. These robust
results across diverse datasets highlight the generalization
of our methods, making them particularly attractive for
resource-limited devices and for reducing the power
consumption of machine learning models.
We also introduce Virtual Coordinate-based Neural Networks
(VCNN), a novel machine learning approach that utilizes
Virtual Coordinates (VCs) as node embeddings. VCs are
computed as distances from nodes to a set of randomly
selected anchor nodes, providing an efficient representation
of graph topology without the need for feature extraction.
We are currently working on:
