Hierarchical Clustering and Schur Complement for Automatic Hyperspectral Band Selection

Band selection is a crucial step in hyperspectral imaging to reduce spectral redundancy and processing costs whilst retaining information useful for classification. Most existing approaches require the number of bands to be retained to be set manually or rely on parameters that are difficult to adjust. This work proposes the Clustering-Unified Schur complement for Diversity with Hierarchical Clustering (CUSD-HC). This fully unsupervised band selection method combines Ward’s hierarchical clustering with a greedy selection based on the Schur complement. Bands are grouped by spectral similarity, and then a representative band is chosen from each group to preserve diversity and informational content. The number of bands is determined automatically using a multi-detector k-fold criterion combined with an intrinsic dimension threshold estimated via PCA. Evaluated on six benchmark datasets using four classifiers (SVM-RBF, Random Forest, XGBoost, LightGBM), CUSD-HC achieves an average rank of between 2.7 and 3.3 among nine compared methods, placing it consistently among the leading group. The Nemenyi test shows no statistically significant difference between CUSD-HC and the top-ranked competitors, while CUSD-HC significantly outperforms the weakest baselines (p < 0.05); unlike the best-ranked alternatives, it reaches this level of performance without any manual selection of the number of bands, which is determined automatically from the data. An inter-scene transferability experiment on the WHU-Hi datasets shows a maximum degradation of 3.9 points in overall accuracy (OA), and the transferred bands even outperform the native selection in three cases out of six. Furthermore, the selected bands naturally cover the main spectral regions (visible, near-infrared, and SWIR), which facilitates the interpretation of results for applications such as precision agriculture and environmental monitoring.