This article is concerned with quantifying and representing group differences when there are more variables than observations. In particular, canonical variate analysis when the data consist of curves sampled at many grid points is considered. A new method is proposed that involves replacing the usually singular within-groups variation matrix by a fitted matrix that is positive-definite. To obtain the fitted matrix, a class of models, along with associated estimation and model-selection procedures, is presented. The results are applied to experimental data designed to assess the usefulness of data from a portable field spectrometer for discriminating between usable farmland and farmland affected by salinity.