BASIL: Scalable Bayesian Semi-supervised Clustering with Feature Selection and Adaptive Constraint Weighting

Constrained clustering incorporates prior knowledge in the form of pairwise constraints to guide data partitioning. While effective, existing Bayesian approaches are often limited in scalability to large datasets and provide weak interpretability due to the lack of explicit feature relevance modeling. We propose BASIL, a scalable Bayesian semi-supervised clustering framework that leverages stochastic variational inference to jointly infer cluster assignments and feature importance weights. This joint formulation enables the identification of discriminative features consistent with the imposed constraints. To robustly handle noisy or inconsistent supervision, BASIL introduces an adaptive constraint-weighting mechanism that down-weights unreliable constraints. Experiments on synthetic and real-world benchmarks show BASIL attains competitive accuracy while reducing training time by over $96\\%$ on large datasets, learns interpretable cluster-specific feature importance maps, and remains robust to up to $30\\%$ noisy constraints under sufficient supervision. We further demonstrate applicability to large-scale health data, including medical imaging and electronic health records.