  In high reliability standards fields such as automotive, avionics or
aerospace, the detection of anomalies is crucial. An efficient methodology for
automatically detecting multivariate outliers is introduced. It takes advantage
of the remarkable properties of the Invariant Coordinate Selection (ICS)
method. Based on the simultaneous spectral decomposition of two scatter
matrices, ICS leads to an affine invariant coordinate system in which the
Euclidian distance corresponds to a Mahalanobis Distance (MD) in the original
coordinates. The limitations of MD are highlighted using theoretical arguments
in a context where the dimension of the data is large. Unlike MD, ICS makes it
possible to select relevant components which removes the limitations. Owing to
the resulting dimension reduction, the method is expected to improve the power
of outlier detection rules such as MD-based criteria. It also greatly
simplifies outliers interpretation. The paper includes practical guidelines for
using ICS in the context of a small proportion of outliers which is relevant in
high reliability standards fields. The choice of scatter matrices together with
the selection of relevant invariant components through parallel analysis and
normality tests are addressed. The use of the regular covariance matrix and the
so called matrix of fourth moments as the scatter pair is recommended. This
choice combines the simplicity of implementation together with the possibility
to derive theoretical results. A simulation study confirms the good properties
of the proposal and compares it with other scatter pairs. This study also
provides a comparison with Principal Component Analysis and MD. The performance
of our proposal is also evaluated on several real data sets using a
user-friendly R package accompanying the paper.
