Two practical realities constrain the analysis of microarray data, mass spectra from proteomics, and biomedical infrared or magnetic resonance spectra. One is the curse of dimensionality: the number of features characterizing these data is in the thousands or tens of thousands. The other is the curse of dataset sparsity: the number of samples is limited. The consequences of these two curses are far-reaching when such data are used to classify the presence or absence of disease.