🤖 AI Summary
Existing deep constrained clustering (DCC) methods suffer from anchor dependency or insufficient discriminability of Euclidean embeddings, limiting scalability and practical applicability. To address these issues, we propose SpherePair—a spherical-geometric angle-constrained embedding framework that models pairwise constraints as angular relationships on the unit hypersphere, thereby decoupling representation learning from clustering. Its core is the SpherePair Loss, a theoretically grounded contrastive loss defined on the sphere: it requires no pre-specified number of clusters, ensures constraint consistency, supports incremental sample generalization, enables rapid cluster-number inference, and guarantees convergence. Jointly optimized with deep neural networks, SpherePair achieves state-of-the-art performance across multiple benchmark datasets. The method delivers superior clustering accuracy, strong scalability to large-scale data, and robustness for real-world deployment.
📝 Abstract
Constrained clustering integrates domain knowledge through pairwise constraints. However, existing deep constrained clustering (DCC) methods are either limited by anchors inherent in end-to-end modeling or struggle with learning discriminative Euclidean embedding, restricting their scalability and real-world applicability. To avoid their respective pitfalls, we propose a novel angular constraint embedding approach for DCC, termed SpherePair. Using the SpherePair loss with a geometric formulation, our method faithfully encodes pairwise constraints and leads to embeddings that are clustering-friendly in angular space, effectively separating representation learning from clustering. SpherePair preserves pairwise relations without conflict, removes the need to specify the exact number of clusters, generalizes to unseen data, enables rapid inference of the number of clusters, and is supported by rigorous theoretical guarantees. Comparative evaluations with state-of-the-art DCC methods on diverse benchmarks, along with empirical validation of theoretical insights, confirm its superior performance, scalability, and overall real-world effectiveness. Code is available at href{https://github.com/spherepaircc/SpherePairCC/tree/main}{our repository}.