Hyperspectral remote sensing is recognized as a powerful tool for mineralogical mapping of exposed surfaces on Earth and planets, as well. It allows for more rigorous discrimination among materials than multispectral imaging. Nevertheless, the huge data volume that comes with single observations results in severe limitations to successful data exploitation. Many techniques of feature reduction that have been developed so far do not allow for the complete exploitation of the informational content of the hyper-dimensional space. The present investigation aims at providing a feature reduction technique that preserves the spectral information and improves the classification results. We accomplished the feature reduction of synthetic and real hypercubes through exponential Gaussian optimization (EGO) and compared the results of k-means, spectral angle mapper (SAM), support vector machines (SVMs), and CLUES clustering techniques. The results show that the k-means clustering of hyper-dimensional spaces is the most efficient technique, but it does not automatically retrieve the optimal number of clusters. The SAM and SVM techniques give discrete results in terms of data partitioning, although the process of endmembers’ selection is challenging and the definition of model parameters is not trivial. The combination of EGO modeling and CLUES algorithm allows for correctly estimating the number of clusters and deriving the accurate partitions when the cluster separability lies on two variables, at least. With real data, the CLUES clustering in the reduced space allows for higher overall performances than the more conventional techniques, although it underestimates the number of categories.