Anchor–Procrustes Consensus Classification (APCC): A cross-year Sentinel-2 framework for land surface classification

Anchor–Procrustes Consensus Classification (APCC) is a Sentinel-2 workflow for land-surface type mapping that enforces cross-year comparability while retaining temporal dynamics. For each year, Sentinel-2 L2A spectral indices are generated as rasters and geometrically harmonized (common projection, pixel size, aligned grid, and extent) to ensure pixel-to-pixel correspondence. A shared predictor set is defined by intersecting index names across years, and pooled scaling is estimated from a combined pixel sample so that the same centering and scaling parameters are applied to each annual stack. In the pooled-scaled space, APCC performs two-level spectral structuring. First, PCA captures dominant shared gradients (PC1–PC2) and hierarchical clustering is applied to PCA scores, with k selected by the Calinski–Harabasz criterion; the resulting centroids define a reproducible level-1 nearest-centroid rule that is propagated to rasters. Second, finer contrasts are extracted by removing the PC1–PC2 explained component from each index and running residual PCA (rPCA) on the residual matrix. Level-1 clusters are evaluated for homogeneity in rPC space, and heterogeneous clusters are refined by nearest-centroid splitting using rPC coordinates, yielding a consistent set of primary and refined classes. Temporal invariance is introduced through anchor pixels. Within each class and year, core pixels are selected as cells closest to the class centroid, and anchor pixels are defined as the intersection of core and invariant pixels between years. Procrustes/GPA is fitted on anchor feature matrices to estimate year→consensus transformations (translation, rotation, scaling) and to construct a consensus configuration of spectral archetypes. The fitted transformations are applied to annual stacks, mapping every pixel into a consensus feature space. Final classification is performed in this consensus-aligned space by estimating class means from anchor pixels and assigning all pixels by minimizing pooled Mahalanobis distance using a pooled within-class covariance with ridge regularization. APCC is implemented in R code with alignment and automated change-diagnostic outputs.