An efficient method to estimate the optimum regularization parameter in RLDA

The biomarker discovery process in high-throughput genomic profiles has presented the statistical learning community with a challenging problem, namely learning when the number of variables is comparable or exceeding the sample size. In these settings, many classical techniques including linear discriminant analysis (LDA) falter. Poor performance of LDA is attributed to the ill-conditioned nature of sample covariance matrix when the dimension and sample size are comparable. To alleviate this problem, regularized LDA (RLDA) has been classically proposed in which the sample covariance matrix is replaced by its ridge estimate. However, the performance of RLDA depends heavily on the regularization parameter used in the ridge estimate of sample covariance matrix.