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Angular Constraint Embedding via SpherePair Loss for Constrained Clustering
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Proposes SpherePair, an anchor-free deep constrained clustering method that embeds pairwise constraints via a cosine-similarity logistic loss in angular space, with theory on the negative-zone factor and PCA-based cluster-number inference.
Problem
Deep constrained clustering from pairwise must-link/cannot-link constraints struggles with anchor misalignment in end-to-end methods and with Euclidean margin tuning and unbounded distances in constraint embedding; it also requires knowing the number of clusters.
Approach
An anchor-free angular pairwise loss: positives are pulled to small angles while negatives are pushed to an angular negative zone of size pi/omega with omega=2 fixed by theory; a reconstruction regularizer on normalized embeddings is added, and K is inferred from a plateau in PCA-subspace minimal inter-cluster angles.
Key results
- SpherePair ranks first in over 60 of 72 comparisons (8 datasets x 3 constraint levels x 3 metrics) against DCC baselines.
- On CIFAR-100-20 with 10k constraints, SpherePair reaches 62.8% test ACC versus 60.5% for the next best (AutoEmbedder).
- On RCV1-10 with 10k constraints, SpherePair reaches 91.8% ACC; cluster-number inference on CIFAR-100-20 estimates K within 18-22 for true K=20.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SpherePair instead of CIDEC | CIFAR100-20 constrained clustering with 1k constraints · CIFAR100-20, 1k constraints test | ACC: 46.2 -> 48.2 | Helped |
| Use SpherePair instead of CIDEC | CIFAR10 constrained clustering with 1k constraints · CIFAR10, 1k constraints test | ACC: 86.5 -> 85.6 | Hurt |
| Use SpherePair instead of DCGMM | FashionMNIST constrained clustering with 1k constraints · FashionMNIST, 1k constraints test | ACC: 63.5 -> 69.8 | Helped |
| Use SpherePair instead of DCGMM | ImageNet-10 constrained clustering with 1k constraints · ImageNet-10, 1k constraints test | ACC: 94.4 -> 95.9 | Helped |
| Use SpherePair instead of CIDEC | MNIST constrained clustering with 1k constraints · MNIST, 1k constraints test | ACC: 88.0 -> 91.7 | Helped |
| Use SpherePair instead of SpherePair without pretraining (ablation) | Reuters subset constrained clustering with 1k constraints · Reuters subset, 1k constraints test | ACC: 86.0 -> 91.4 | Helped |
| Use SpherePair instead of CIDEC | STL-10 constrained clustering with 1k constraints · STL-10, 1k constraints test | ACC: 87.8 -> 88.1 | Helped |
| Use SpherePair instead of VolMax-DCC | RCV1-10 constrained clustering with 1k constraints · RCV1-10, 1k constraints test | ACC: 49.9 -> 65.8 | Helped |
| Add pretraining to SpherePair (ablation) | SpherePair constrained clustering · Most datasets, 1k constraints test | ACC: 45.1 -> 48.2 (CIFAR100-20); 84.2 -> 85.6 (CIFAR10); 62.1 -> 69.8 (FashionMNIST); 95.6 -> 95.9 (ImageNet-10); 71.0 -> 91. | Helped |
Surprising findings
- The unpretrained SpherePair variant still beats CIDEC without pretraining by about 10-20% on most datasets.
- Baseline performance degrades as constraint imbalance increases, even though imbalanced sets contain more constraints.
Limitations
- Supports only single-view unstructured data.
- Does not address incomplete or noisy constraint annotations.
Experimental setup
Datasets: CIFAR-100-20 CIFAR-10 FashionMNIST ImageNet-10 MNIST STL-10 Reuters subset RCV1-10
Benchmarks: CIFAR-100-20 CIFAR-10 FashionMNIST ImageNet-10 MNIST STL-10 Reuters RCV1-10
Metrics: ACC NMI ARI
Baselines: VanillaDCC VolMaxDCC DCGMM CIDEC SDEC AutoEmbedder
Builds on: AutoEmbedder CPAC MCL loss VanillaDCC CIDEC
Closest papers by meaning
- Uncertainty-Aware Probabilistic Constrained Clustering from Entangled Pairwise Supervision (NeurIPS 2026 · similarity 0.86)
- Towards Better-than-2 Approximation for Constrained Correlation Clustering (ICML 2025 · similarity 0.84)
- THESAURUS: Contrastive Graph Clustering by Swapping Fused Gromov-Wasserstein Couplings (AAAI 2025 · similarity 0.84)
- A Hubness Perspective on Representation Learning for Graph-Based Multi-View Clustering (CVPR 2025 · similarity 0.84)
- You Can Trust Your Clustering Model: A Parameter-free Self-Boosting Plug-in for Deep Clustering (NeurIPS 2025 · similarity 0.84)
- Exploring a Principled Framework for Deep Subspace Clustering (ICLR 2025 · similarity 0.83)
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