Regularized sliced inverse regression with applications in classification

Consider the problem of classifying a number of objects into one of several groups or classes based on a set of characteristics. This problem has been extensively studied under the general subject of discriminant analysis in the statistical literature, or supervised pattern recognition in the machine learning field. Recently, dimension reduction methods, such as SIR and SAVE, have been used for classification purposes. In this paper we propose a regularized version of the SIR method which is able to gain information from both the structure of class means and class variances. Furthermore, the introduction of a shrinkage parameter allows the method to be applied in under-resolution problems, such as those found in gene expression microarray data. The REGSIR method is illustrated on two different classification problems using real data sets.