Feature selection in omics prediction problems using cat scores and false non-discovery rate control

We revisit the problem of feature selection in linear discriminant analysis (LDA), i.e. when features are correlated. First, we introduce a pooled centroids formulation of the multi-class LDA predictor function, in which the relative weights of Mahalanobis-transformed predictors are given by correlation-adjusted t-scores (cat scores). Second, for feature selection we propose thresholding cat scores by controlling false non-discovery rates (FNDR). Third, training of the classifier is based on James-Stein shrinkage estimates of correlations and variances, where regularization parameters are chosen analytically without resampling. Overall, this results in an effective and computationally inexpensive framework for high-dimensional prediction with natural feature selection. The proposed shrinkage discriminant procedures are implemented in the R package ``sda'' available from the R repository CRAN.