Regularized Discriminant Analysis and Its Application in Microarray

In this paper, we introduce a family of some modified versions of linear discriminant analysis, called “shrunken centroids regularized discriminant analysis” (SCRDA). These methods generalize the idea of the nearest shrunken centroids of Prediction Analysis of Microarray (PAM) into the classical discriminant analysis. These SCRDA methods are specially designed for classification problems in high dimension low sample size situations, for example microarray data. Through both simulation study and real life data, it is shown that these SCRDA methods perform uniformly well in the multivariate classification problems, especially outperform the currently popular PAM. Some of them are also suitable for feature elimination purpose and can be used as gene selection methods. The open source R codes for these methods are also available and will be added to the R libraries in the near future.