k-Nearest Neighbors Classification Using Gromov-Wasserstein Distance
A new preprint introduces k-nearest neighbors (k-NN) classifiers built on the Gromov–Wasserstein (GW) and fused Gromov–Wasserstein (fGW) distances, and formally proves their universal consistency for graph classification. GW distance allows direct comparison of graphs with differing numbers of nodes without requiring a common embedding, and the fGW variant additionally incorporates node features. The theoretical guarantees, backed by numerical experiments across multiple graph datasets, suggest this framework could offer a principled and broadly applicable approach to graph classification.
Researchers have proposed using the Gromov–Wasserstein (GW) distance as the basis for k-nearest neighbors (k-NN) classification of graph-structured data, presenting both theoretical proofs and empirical validation in a preprint submitted to arXiv. The GW distance compares metric measure spaces independently of their underlying geometry or size, making it well-suited for graphs that may have different numbers of nodes. The authors prove universal consistency of the GW-k-NN classifier on the space of equivalence classes of finitely supported metric measure spaces with uniform probability measures, which directly covers the space of graphs when nodes are treated as uniformly weighted points with pairwise distances. They extend this result to the fused GW (fGW) variant, proving universal consistency on spaces of node-attributed graphs by incorporating Euclidean-valued feature maps alongside structural information. Numerical experiments across several benchmark graph datasets confirm that both GW-k-NN and fGW-k-NN perform consistently well, supporting the practical viability of metric-based classifiers in the GW framework. The work bridges optimal transport theory and machine learning, providing formal statistical guarantees for a class of graph classifiers that require no graph embedding or preprocessing.
What's missing
The study does not report computational complexity or runtime benchmarks comparing GW-k-NN and fGW-k-NN against existing graph classification methods, which is a notable practical consideration given the known computational cost of GW distance computations.
What different sources said
- arXiv cs.LGCenter
$k$-Nearest Neighbors in Gromov--Wasserstein Space
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