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WatE: A Wasserstein t-distributed Embedding Method for Information-enriched Graph Visualization

AAAI 2025 · Graph learning › Graph algorithms and clustering · approach: Graph embedding and spectral sparsification · 0 citations (OpenAlex)

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Proposes WatE, a GNN-based inductive graph visualization method that represents each graph as an ellipse (mean and covariance of node embeddings) learned via a regularized t-SNE framework using Wasserstein distances.

Problem

Visualizing a set of graphs in a low-dimensional space while preserving both graph-level clustering structure and node-level structural information, in an inductive manner.

Approach

Each graph is embedded as the mean and covariance of its GNN node-embedding distribution, visualized as an ellipse; graph affinities use a Wasserstein-based Student's t-distribution fit to an FGW-based data affinity, with a Gromov-Wasserstein spectral clustering loss and a covariance energy regularizer.

Key results

• On clustering with K=8 (mean and covariance), WatE reaches 93.21% Rand Index on AIDS, 71.91% on MUTAG, and 52.47% on IMDB-B, best on three of four datasets.
• WatE with K=2 (2D mean only) achieves 91.14% on AIDS, competitive with GNN baselines that use 96-160 dimensions.
• Stability: performance stays steady for 0.1 ≤ α ≤ 10 and 1 ≤ β ≤ 100; the covariance regularizer is needed for concentric node-embedding ellipses.

Measured effects reported in the paper

Surprising findings

• On PTC-MR, WatE does not outperform baselines (50.55% vs. 51.64% for GDL), attributed to graphs with different labels but similar structures making the FGW affinity noisy.

Limitations

• Sensitive to noisy affinity when FGW distance does not reflect label differences (PTC-MR).
• Clustering performance on PTC-MR is limited relative to baselines.
• Ellipse visualization is limited to 2D; higher-dimensional embeddings need PCA projection.

Experimental setup

Datasets: IMDB-B MUTAG PTC-MR AIDS

Benchmarks: IMDB-B MUTAG PTC-MR AIDS

Metrics: Rand Index (%)

Baselines: RWK SPK GK WLK FGWK GWF GDL GraphCL ADGCL

Builds on: t-SNE Wasserstein t-SNE fused Gromov-Wasserstein distance GraphCL Gromov-Wasserstein factorization

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