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.

Doctors, biologists, and analysts often need to sort large collections of items into meaningful groups, for example grouping patients by health profile or images by content. Pure data-driven grouping ignores what experts already know, while rule-based grouping ignores patterns in the data. Combining the two is the best approach. Existing combined methods struggle when the data is huge, when some expert hints are wrong, or when it is unclear which features actually drive the grouping. We introduce BASIL, a method that groups items using both the data and pairs of items that experts mark as "should belong together" or "should not belong together." BASIL also identifies which characteristics matter most for each group, and automatically down-weights expert hints that look inconsistent with the rest of the data. It scales to very large datasets, including over half a million UK patient health records. In our experiments, BASIL trains in hours where competing methods take days, stays accurate when up to a third of the expert hints are wrong, and produces interpretable summaries of each group. Applied to UK primary-care records, it identified patient subgroups with markedly different risks of hospitalisation and mortality, suggesting it could help direct care to those who need it most.