SCoRP: Soft Consensus and Residual KL Projection for Feasible Clustering

Frozen foundation representations often make simple clustering methods competitive, but converting their outputs into stable, feasible hard partitions remains difficult. Soft assignments preserve uncertainty but may lose requested clusters after rowwise decoding; early hard pseudo-labels can amplify errors; and strict equipartition can distort imbalanced data. We introduce Soft Consensus and Residual Projection (SCoRP), a label-free soft-to-hard partition operator for fixed feature representations. It aligns multiple seed partitions into a soft consensus, propagates that consensus with a stochastic graph resolvent, estimates an adaptive cluster-mass target, and applies an anchored residual generalized Kullback–Leibler (GKL) projection before a decoder that restores feasibility with the minimum number of changes to the unconstrained rowwise-argmax partition. We establish joint graph–posterior perturbation stability, uniqueness and strict convexity of the reduced projection problem, an exact generalized-KL projection identity, exact soft mass control, minimum-Hamming hard feasibility, set-valued label-permutation equivariance with a conditional pointwise guarantee, and a sufficient neighborhood-preservation condition for optional bounded Confidence-Refined Adaptive Feature Transformation (CRAFT). An 18-dataset audit spans image, text, tabular, and sensor data and retains favorable and unfavorable outcomes. Representative clustering-accuracy (ACC) changes against the strongest standard same-feature baseline are +3.91 points on CIFAR-10, +3.15 on CIFAR-100, +1.64 on EuroSAT, and +8.61 on COIL-20. The mixed results support SCoRP as a controlled soft-to-hard partition operator when the supplied representation is informative, not as a universal remedy for inadequate feature geometry.