Research map / Learning theory and algorithms / Optimal transport
An Optimal Transport View for Subspace Clustering and Spectral Clustering
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Explains subspace and spectral clustering through a self entropic optimal transport view and proposes SOTA/SFGW models that learn coupled affinity matrices and spectral embeddings via fused Gromov-Wasserstein barycenters.
Problem
Clustering methods such as spectral and subspace clustering lack a unified explanation, and learning the affinity matrix and spectral embeddings jointly has not been connected to optimal transport.
Approach
A self entropic optimal transport plan over one group of samples (with zero diagonal) serves as a normalized affinity matrix, linking subspace clustering (self-expressiveness via barycentric mapping) and spectral clustering (Stiefel-manifold embeddings); the spectral OT barycenter model then jointly optimizes features, metric (Gromov-Wasserstein) information, and optionally sample weights for outl
Key results
- SFGWH achieves 96.7 accuracy on iris versus 90.7 for spectral clustering and 95.9 for ERCAN, and 73.7 on ecoli versus 69.1 for ERCAN.
- On landsat, SFGWH reaches 68.3 accuracy versus 51.0 for ERCAN, the strongest gain reported in the no-outlier setting.
- With the smallest clusters treated as outliers, SFGW obtains the best outlier-recall on ecoli (55.6), glass (41.0), landsat (46.9), seeds (48.6), and zoo (33.3) among compared methods.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Spectral OT barycenter (SFGWH) instead of ERCAN / SC on UCI datasets without outliers | spectral clustering · UCI six datasets, accuracy | accuracy | Mixed |
| Adding learnable marginal / OT-based outlier handling (SFGW) for clustering with outliers | SFGW · UCI with smallest clusters as outliers, outlier recall | outlier recall | Mixed |
| Affinity from self entropic OT (Gaussian kernel with zero diagonal) used for spectral clustering | spectral clustering · simulation data | qualitative reconstruction | No clear effect |
| Tuning λX and λH on iris (ablation) | SFGWH · iris | accuracy | Mixed |
Surprising findings
- On zoo, SFGWH (68.9 accuracy) underperforms ERCAN (75.2), so the proposed method is not uniformly best.
Limitations
- Experiments are limited to small UCI benchmarks and a single two-cluster simulation.
- Performance is sensitive to the trade-off parameter lambda_X, and the metric-learning term is only described for one implementation.
- The Gromov-Wasserstein term uses fixed cosine-similarity metrics on features rather than learned embeddings.
Experimental setup
Datasets: ecoli glass iris landsat seeds zoo
Benchmarks: UCI ecoli UCI glass UCI iris UCI landsat UCI seeds UCI zoo
Metrics: accuracy NMI outlier recall
Baselines: K-means spectral clustering ERCAN K-means– COR FCM
Builds on: Sinkhorn entropic optimal transport fused Gromov-Wasserstein spectral clustering ERCAN
Closest papers by meaning
- Transport Clustering: Solving Low-Rank Optimal Transport via Clustering (ICML 2026 · similarity 0.88)
- Co-clustering through Optimal Transport (ICML 2017 · similarity 0.88)
- Double-Bounded Optimal Transport for Advanced Clustering and Classification (AAAI 2024 · similarity 0.87)
- One-Step Spectral Clustering via Dynamically Learning Affinity Matrix and Subspace (AAAI 2017 · similarity 0.86)
- Learning Ultrametric Trees for Optimal Transport Regression (AAAI 2024 · similarity 0.85)
- Low-Rank Optimal Transport through Factor Relaxation with Latent Coupling (NeurIPS 2024 · similarity 0.85)
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