Exploring Data via Invariant Coordinate Selection in R, Python, and Julia

Abstract

Invariant Coordinate Selection (ICS) is a powerful unsupervised multivariate method designed for identifying the structure of multivariate datasets on a subspace. It goes beyond the well-known Principal Components Analysis method by not relying on maximizing the inertia but on optimizing a generalized kurtosis and is not only invariant by orthogonal transformation of the data but by any affine transformation. More precisely, ICS compares two scatter matrices through their joint diagonalization. Some theoretical results proved that under some elliptical mixture models, the subspace spanned by the first and/or last components carries the information regarding the multivariate structure and recovers the Fisher discriminant subspace, whatever the choice of scatter matrices. Among others, we studied the relevance of ICS for outlier detection and clustering purposes from a theoretical and empirical point of view. In this article, we discuss the recent overhaul of the ICS package in R, describe related R packages that together form an ICS-oriented ecosystem, and provide an overview of recent implementations of ICS in Python and Julia.