On the usage of joint diagonalization in multivariate statistics: Speed presentation April 2022

Abstract

In principal component analysis, one scatter matrix such as the covariance matrix is diagonalized. In case the data follows an elliptical distribution, all scatter matrices are proportional and the choice of the scatter matrix does not matter much. Outside the elliptical model, different scatter matrices estimate different population quantities and the comparison of different scatter matrices is of interest. In this talk, we provide an overview of how joint diagonalization of two or more scatter matrices can be used and how this helps for unsupervized data exploration. We first give details on the unsupervized dimension reduction method called Invariant Coordinate Selection which makes use of simultaneous diagonalization of two scatter matrices in a model free context. We also present Blind Source Separation models where the joint diagonalization of two or more scatter matrices plays an important role for different types of data including time series and spatial random fields.