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Joint Hierarchical Representation Learning of Samples and Features via Informed Tree-Wasserstein Distance

NeurIPS 2025 · Graph learning › Graph self-supervised learning · approach: Multi-view graph clustering · 0 citations (OpenAlex)

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Proposes an iterative alternating scheme that builds hyperbolic/diffusion-based trees for samples and features, computing tree-Wasserstein distances across modes, optionally refined by Haar wavelet filtering, and uses the learned sample tree to initialize HGCNs.

Problem

Hierarchical structure often exists in both samples and features of a data matrix, but existing hierarchical representation methods model only one mode at a time.

Approach

Alternately build a tree for one mode, compute tree-Wasserstein distances for the other mode using that tree, and rebuild the tree from those distances; add data-driven Haar wavelet filtering from the learned trees at each iteration, with convergence guarantees.

Key results

• On word-document and scRNA-seq sparse approximation, the proposed methods achieve the lowest Haar L1 norms, e.g., CBMC sample L1 of 489.4 vs. 926.8 for the best baseline Co-TR-TWD.
• Document and single-cell kNN classification: proposed method reaches 97.3% on BBCSPORT and 94.0% on ZEISEL, above baselines such as QUE at 91.6% and 83.6%.
• Integrated as preprocessing in HGCN, it improves link prediction on DISEASE to 98.4 AUC vs. 90.8 for HGCN and node classification on CORA to 83.9 vs. 79.9.

Measured effects reported in the paper

Surprising findings

• Applying wavelet filters with trees from other TWD baselines does not consistently improve tree quality, the authors argue because those trees approximate Wasserstein distance rather than hierarchy.
• Wavelet filters alone without the iterative scheme do not yield comparable gains for HGCNs.

Limitations

• Trees may not represent data on complex geometries such as spherical manifolds, mixed-curvature spaces, asymmetric data, or general graphs.
• Convergence theorem requires strictly positive regularization (gamma > 0), while practice uses gamma = 0.
• Method is not differentiable, so it cannot be directly integrated into neural architectures.

Experimental setup

Datasets: BBCSPORT TWITTER CLASSIC AMAZON ZEISEL CBMC CORA PUBMED DISEASE AIRPORT

Benchmarks: BBCSPORT TWITTER CLASSIC AMAZON ZEISEL CBMC CORA PUBMED DISEASE AIRPORT

Metrics: L1 norm of Haar coefficients kNN classification accuracy ROC AUC F1 score accuracy

Baselines: Co-Quadtree Co-Flowtree Co-UltraTree Co-TSWD Co-SWCTWD Co-SWQTWD QUE Tree-WSV WSV HGCN H2H-GCN GCN

Builds on: Tree-Wasserstein distance Tree-WSV Wasserstein singular vectors HGCN diffusion geometry tree construction

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