Invariant Coordinate Selection: An Overview and Recent Developments

Abstract

Many classical multivariate statistical methods have been established for decades. Among more recent developments, Invariant Coordinate Selection (ICS) has emerged as a powerful and unifying framework. ICS jointly diagonalizes two scatter matrices, encompassing various traditional methods as special cases. It has evolved into a comprehensive multivariate technique, applied in descriptive statistics and dimension reduction, and used as a transformation-retransformation procedure. ICS is particularly effective for dimension reduction in tasks such as outlier detection and clustering, as it can recover Fisher’s linear discriminant subspace without requiring prior knowledge of class labels. Within the independent component analysis (ICA) framework, ICS also serves as a tool for identifying independent components. This review provides an overview of ICS, including its diverse applications, recent extensions, and available software for practical implementation.