Multivariate functional anomaly detection has received a large amount of attention recently. Accounting both the time dimension and the correlations between variables is challenging due to the existence of different types of outliers and the dimension of the data. In the context of predictive maintenance and quality control, data sets often contain a large number of functional variables. However, most of the existing methods focus on a small number of functional variables. Moreover, in fields that have high reliability standards, detecting a small number of potential multivariate functional outliers with as few false positives as possible is crucial. In such a context, the adaptation of the Invariant Coordinate Selection (ICS) method from the multivariate to the multivariate functional case is of particular interest. Two extensions of ICS are proposed: point-wise and global. For both methods, the choice of the relevant components together with outlier identification and interpretation are discussed. A comparison is made on a predictive maintenance example from the avionics field and a quality control example from the microelectronics field. It appears that in such a context, point-wise and global ICS with a small number of selected components can be recommended.
We would like to thank the Associate Editor and two reviewers for their suggestions and comments that helped us a lot to improve the paper. This work was partly supported by the French Agence Nationale de la Recherche through CIFRE contract 2017/1354 and through the Investments for the Future (Investissements d’Avenir) program, grant ANR-17-EURE-0010, the Academy of Finland (Grant 335077) and by a grant of the Dutch Research Council (NWO, research program Vidi, project number VI.Vidi.195.141). The authors are grateful to Camille Girou for some preliminary work on the semiconductor data set and to Martina Salvignol for her help on the aeronautical data set.
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