Components selection for multivariate outlier detection with ICS

Abstract

The detection of a small proportion of multivariate outliers such as identifying production errors in industrial processes is an important topic. In this context, the Invariant Coordinate Selection (ICS) method is an efficient identification procedure. The ingenious idea of the method, compared to other multivariate methods such as Principal Component Analysis (PCA) or robust PCA, is to simultaneously diagonalize two scatter matrices. In case of a small percentage of outliers, the ICS coordinates are ordered decreasingly according to a generalized concept of kurtosis depending on the considered pair of scatters. Taking into account the coordinates associated with large kurtosis values, the observations far away from the center of the data are declared as outliers. One challenging step in the procedure is to select the components that display outliers. Two approaches are introduced and compared. The first one is comparable to a test procedure where the critical value is calculated using some simulations. The other approach incorporates some univariate normality tests. The first approach is time consuming and depends on the sample size, the dimension and the pair of scatters involved in ICS. Some approximations are thus constructed in order to avoid to carry out new simulations for each case.