Evaluation of Internal Cluster Validity Indices for Selecting the Number of K-Means Clusters in Sentinel-2 Imagery
Keywords:
K-means, Cluster number selection, Internal cluster validity, Sentinel-2, LUCASAbstract
Selecting the number of clusters is a central methodological decision in unsupervised analysis of multispectral imagery. This study evaluated the Silhouette coefficient, Calinski-Harabasz index, Davies-Bouldin index, and gap statistic for K-means clustering of harmonised Sentinel-2 Level-2A growing-season composites. Three 50 × 50 km study windows in Spain and Cyprus were analysed using two feature representations: six surface-reflectance bands and the same bands augmented with NDVI, MNDWI, NBR, and BSI. Candidate solutions containing 2-12 clusters were compared with an aggregated LUCAS Copernicus 2018 reference legend using V-measure, assessed for stability across 20 fits to 80% pixel subsamples, and examined with a chance-corrected eight-neighbour agreement coefficient. Silhouette selected two clusters in all six window-by-feature combinations. Calinski-Harabasz selected two clusters in five combinations, whereas Davies-Bouldin produced interior minima in two. The gap statistic did not satisfy its one-standard-error stopping rule within the evaluated range. The V-measure optimum varied among 2, 4, 6, 7, and 11 clusters, and no internal criterion matched it in every combination. The maximum V-measure ranged from 0.213 to 0.590. The three compactness-and-separation criteria had similar median agreement losses (0.115-0.127), but losses varied substantially among windows and reached 0.286. The adjusted Rand index identified the same agreement optimum as V-measure in five of six combinations. Stability was generally high but showed pronounced local reductions in two index-selected solutions. At matched cluster numbers, adding spectral indices increased local neighbour agreement in 27 of 33 comparisons. For the examined scenes, internal validity alone did not consistently identify the partition with the highest thematic agreement. Index curves, thematic agreement, and subsampling stability should therefore be considered together when selecting the number of clusters.
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