Persons at risk for Alzheimer's disease (AD) demonstrate altered cortical activation measured by functional MRI (fMRI) years before symptoms of disease are expected. We used fMRI to study the differences in cortical activation between 13 women with a family history of AD and at least one apolipoprotein E4 allele, a risk factor for AD, and a control group of 11 women lacking both factors. Our primary goal was to assess how well the two groups are able to be statistically separated, a task which directly affects the performance of post hoc classification. The dimension of the dataset, however, precludes the use of ordinary classification methods. In this paper we show the superiority of using oriented PLS (OrPLS) to accomplish the classification in the presence of this dimensionality problem. We are able to reduce the misclassification rates on the standardized fMRI data from an average of about 48% for PCA, to an average of 27% for PLS, and then to perfect classification for OrPLS.