New algorithms for implementing invariant component selection

Abstract

ICS (Invariant Component Selection) is a method for multivariate analysis based on the joint diagonalization of two scatter matrices. In the statistics literature, it is usually just stated that it can be solved as a generalized eigenvalue-eigenvector problem and little details about the actual computations are given. Some implementations in R are for example in the R packages ICS and ICtest. However, the existing functions do not take into account singular or nearly singular scatter matrices. In particular, in the case of nearly singular matrices, the existing algorithms do work but may encounter numerical instability. The aim is to propose alternative implementations of ICS and compare them to the existing ones.