MAGIC: Multi-Affinity Gaussian Iterative Clustering

We present MAGIC (Multi-Affinity Gaussian Iterative Clustering), a hybrid clustering algorithm that fuses three complementary affinity signals (Gaussian probabilistic fit, density compatibility, and centroid geometry) through an adaptive weighting mechanism that evolves across iterations. Unlike K-means, which assumes spherical clusters, or HDBSCAN, which can misclassify sparse-but-valid structure as noise under heterogeneous local-density regimes, MAGIC measures density compatibility relative to each cluster's empirical density distribution. On datasets with structurally different local density profiles, MAGIC achieves mean ARI 0.869 (10-seed) versus HDBSCAN's 0.004 and K-means' 0.678. Ablation analysis shows Gaussian and centroid affinities are the primary accuracy drivers, while density affinity contributes as a system-level regularizer within the fusion rather than a standalone accuracy signal. Across fourteen synthetic and real-world datasets, MAGIC outperforms K-means on 8/14, matches GMM on Gaussian-structured data (GMM leads or ties on 9/14), and substantially outperforms HDBSCAN under mixed-density conditions, while an honest performance boundary shows all three affinities are structurally blind to path-connectivity topology. We motivate and evaluate a deployment context in hospital command center operations, where routine events form dense clusters and rare surge-precursor events form sparse ones, exactly the failure regime density-connectivity methods mishandle.