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We revisit the problem of feature selection in linear discriminant analysis(LDA), that is, when features are correlated. First, we introduce a pooledcentroids formulation of the multiclass LDA predictor function, in which therelative weights of Mahalanobis-transformed predictors are given bycorrelation-adjusted $t$-scores (cat scores). Second, for feature selection wepropose thresholding cat scores by controlling false nondiscovery rates (FNDR).Third, training of the classifier is based on James--Stein shrinkage estimatesof correlations and variances, where regularization parameters are chosenanalytically without resampling. Overall, this results in an effective andcomputationally inexpensive framework for high-dimensional prediction withnatural feature selection. The proposed shrinkage discriminant procedures areimplemented in the R package ``sda'' available from the R repository CRAN.

Feature selection in omics prediction problems using cat scores and false nondiscovery rate control