Numerical Considerations and a New Implementation for Invariant Coordinate Selection

Invariant Coordinate Selection (ICS) is a multivariate data transformation and dimension reduction method that can be useful in many different contexts. It used for outlier detection or cluster identification, seen as an independent component non-Gaussian analysis method. The usual implementation of ICS based on joint diagonalization two scatter matrices, may numerically unstable some ill-conditioned situations. We focus one-step M-scatter matrices propose new pivoted QR factorization the centered set. This avoids direct computation their inverse brings numerical stability to algorithm. Furthermore, row column pivoting leads rank revealing procedure allows when are not full rank. Several artificial real sets illustrate interest using compared original one.