Title: Multivariate functional outlier detection using invariant coordinate selection
Authors: Anne Ruiz-Gazen - Toulouse School of Economics (France) [presenting]
Aurore Archimbaud - Toulouse School of Economics (France)
Feriel Boulfani - Mathematics institute of Toulouse (France)
Xavier Gendre - ISAE-SUPAERO (France)
Klaus Nordhausen - Vienna University of Technology (Austria)
Joni Virta - Aalto University (Finland)
Abstract: Invariant Coordinate Selection (ICS) is an unsupervised multivariate method based on the joint diagonalization of two scatter matrices. It is a dimension reduction method which leads to outlyingness scores helpful for outlier detection in a multivariate context. Nowadays, more and more data sets are of multivariate functional nature, and various possibilities can be considered to extend the ICS outlier detection method to the multivariate functional framework. As usual in functional data analysis, we consider that the multivariate measurements correspond to functions observed on a discrete set of points in their domain. One possible extension of ICS consists in calculating for each component of the vector of curves, a functional approximation of the observed curves using some suitable basis and a finite number of basis vectors. ICS is then implemented on the stacked vector of the coordinates of the component functions in the basis of interest. Another possible extension is to calculate ICS scores at each domain point and derive some global outlyingness measurements over the domain. The two approaches are compared on several real data examples, including some flight monitoring data from the aeronautics industry.