Adjacent-Partition Agreement for Stability-Based Cluster-Number Selection

Resampling agreement can select a coarse partition that is reproducible under perturbation but changes substantially when the candidate cluster count is increased. This study introduces an adjacent-partition-agreement refinement for cluster-number selection. The refinement supplements resampling stability with the normalized mutual information between adjacent full-data partitions and overrides the stability argmax when that agreement falls sufficiently below the median of the agreement curve. The two margins are fixed for the primary experiments and varied only in the reported sensitivity grid. The rule is evaluated in Consensus-Neighborhood Clustering, which provides a sparse neighborhood-consensus affinity, and with an independent radial-basis-function spectral carrier. On Blobs, the reported protocol changes the selected count from 2 to 4 and the adjusted Rand index (ARI) increases from 0.32 to 0.83; an embedding-protocol ablation shows that this exact count is protocol-sensitive. On Digits, the count changes from 2 to 9 and ARI increases from 0.05 to 0.74. The selection is unchanged in the other tested scenarios, including two hyperspectral cases. A candidate upper bound Kmax remains user-specified, and the Indian Pines range is label-informed. The results support correction of a specific coarse-stability failure mode, not generally superior or range-free cluster-number estimation.