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P$^2$OT: Progressive Partial Optimal Transport for Deep Imbalanced Clustering
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Introduces deep imbalanced clustering and P$^2$OT, a progressive partial optimal transport pseudo-labeling framework solved by a fast scaling algorithm, evaluated on long-tailed CIFAR100, ImageNet-R and iNaturalist subsets.
Problem
Deep clustering assumes balanced classes; pseudo-labeling methods degenerate or fail when the underlying class distribution is imbalanced and pseudo-labels are noisy early in training.
Approach
Formulates pseudo-label generation as partial optimal transport with a KL cluster-size prior (instead of equality) and a progressively increasing total-mass constraint that selects confident samples via weights; reformulates it as unbalanced OT with a virtual cluster and solves it with a fast matrix scaling algorithm.
Key results
- On imbalanced training sets P$^2$OT reaches 38.2 ACC on CIFAR100 (+0.9 over SCAN) and 25.9 ACC on ImageNet-R (+2.4 over SCAN*).
- On iNature100 P$^2$OT gets 44.2 ACC vs 38.7 for SCAN (+5.9 over the next best), and on iNature500 32.2 ACC (+3.2 over SCAN).
- Replacing the progressive KL-based formulation with the OT/POT/UOT variants lowers CIFAR100 ACC to 28.2/33.4/35.9 versus 38.2 for the full method.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use P$^2$OT instead of the strongest baseline | deep imbalanced clustering · CIFAR100 training | ACC: 37.2 -> 38.2 | Helped |
| Use P$^2$OT instead of the strongest baseline | deep imbalanced clustering · ImgNet-R training | F1: 22.8 -> 27.3 | Helped |
| Use P$^2$OT instead of the strongest baseline | deep imbalanced clustering · iNature100 training | ACC: 39.5 -> 44.2 | Helped |
| Use P$^2$OT instead of the strongest baseline | deep imbalanced clustering · iNature100 training | NMI: 68.5 -> 67.0 | Hurt |
| Use P$^2$OT instead of the strongest baseline | deep imbalanced clustering · iNature500 training | ACC: 29.0 -> 32.2 | Helped |
| add the KL constraint (compared with equality-constrained POT) (ablation) | P$^2$OT · CIFAR100 training | ACC: +5.8 | Helped |
| add the KL constraint (compared with equality-constrained POT) (ablation) | P$^2$OT · ImgNet-R training | ACC: +3.8 | Helped |
| add the KL constraint (compared with equality-constrained POT) (ablation) | P$^2$OT · iNature500 training | ACC: +3.6 | Helped |
| add progressive ρ (compared with UOT without progressive ρ) (ablation) | P$^2$OT · CIFAR100 training | ACC: +2.3 | Helped |
| add progressive ρ (compared with UOT without progressive ρ) (ablation) | P$^2$OT · ImgNet-R training | ACC: +3.8 | Helped |
| add progressive ρ (compared with UOT without progressive ρ) (ablation) | P$^2$OT · iNature500 training | ACC: +5.4 | Helped |
| use a fixed ρ instead of increasing ρ (ablation) | P$^2$OT · CIFAR100, ImgNet-R, and iNature500 | ACC | Hurt |
Surprising findings
- SPICE collapses to degenerate solutions on imbalanced data, with ACC as low as 0.74 on iNature1000.
- ARI is misleading under imbalance: IIC and SCAN* get high ARI on imbalanced training sets while performing worse on ACC and NMI.
Limitations
- Progressive ramp-up of rho is a fixed sigmoid schedule tied to iteration count, not adaptive; the authors note decline in weighted precision later in training.
- Pseudo-label methods face difficulty at large scale; on iNature1000 the gains over SCAN are small or negative in NMI.
- Results on ImageNet-R and iNature rely on a single pretrained backbone with only the last block fine-tuned.
Experimental setup
Datasets: CIFAR100 ImageNet-R iNaturalist2018
Benchmarks: CIFAR100 ImageNet-R iNature100 iNature500 iNature1000
Metrics: ACC NMI F1 ARI Head/Medium/Tail ACC
Baselines: DINO BCL IIC PICA SCAN SCAN* CC DivClust SPICE OT POT UOT
Builds on: SCAN Sinkhorn-Knopp / entropic OT (self-labeling) unbalanced optimal transport SLA DINO
Closest papers by meaning
- PROTOCOL: Partial Optimal Transport-enhanced Contrastive Learning for Imbalanced Multi-view Clustering (ICML 2025 · similarity 0.87)
- Learning from Sample Stability for Deep Clustering (ICML 2025 · similarity 0.86)
- ConR: Contrastive Regularizer for Deep Imbalanced Regression (ICLR 2024 · similarity 0.85)
- Double-Bounded Optimal Transport for Advanced Clustering and Classification (AAAI 2024 · similarity 0.85)
- From Logits to Hierarchies: Hierarchical Clustering made Simple (ICML 2025 · similarity 0.84)
- RPSC: Robust Pseudo-Labeling for Semantic Clustering (AAAI 2024 · similarity 0.84)
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