Hyperspectral (HS) data contains spectral response information that provides detailed chemical, moisture, and other descriptions of constituent parts of an item. These new sensor data are useful in USDA product inspection and in automatic target recognition (ATR) applications. However, such data introduces problems such as the curse of dimensionality, the need to reduce the number of features used to accommodate realistic small training set sizes, and the need to employ discriminatory features and still achieve good generalization (comparable training and test set performance). HS produces high-dimensional data; this is characterized by a training set size (Ni) per class that is less than the number of input features (HS λ bands). A new high-dimensional generalized discriminant (HDGD) feature extraction algorithm and a new high-dimensional branch and bound (HDBB) feature selection algorithm are described and compared to other feature reduction methods for two HS product inspection applications. Cross-validation methods, not using the test set, select algorithm parameters.© (2003) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.