M. Hubert, P. Rousseeuw and P. Segaert: Multivariate functional outlier detection

Abstract

Firstly we congratulate the authors on a wonderful paper full of new nice ideas, which can be considered as a major breakthrough in the functional outlier detection using visual procedures. These ideas include a taxonomy of outliers, the definition of bag distance and the centrality-stability plots. Indeed, each of the last two ideas is fundamental in the development of each of the two corresponding procedures to detect multivariate functional outliers introduced in the paper. The first procedure consists in constructing a heat map using the functional bag distance based on the Tukey depth while the second in a scatter-plot based on the skew-adjusted projection depth, SPD, named the centrality-stability plot, CSP. Moreover, both procedures complement themselves because the heat maps are good in detecting all kind of outliers excepting the shape outliers, but those are clearly identified with the CSP’s. Our discussion focus, firstly, on shedding light on the behaviour of the proposed procedures when applied to multivariate functional data whose dimension is entitled to be extremely high. Secondly, a simplification of the CSP is proposed. Furthermore, we encourage the authors to comment on the advantages/disadvantages of applying, what they call, the MFSPD versus, what they call, the 1/(1+ FAO), as the difference between them just lies in the reverse order of the integral and inverse functionals.