Finding Multivariate Outliers With FastPCS

The Projection Congruent Subset (PCS) Outlyingness is a new index of multivariate outlyingness obtained by considering univariate projections of the data. Like many other outlier detection procedures, PCS searches for a subset which minimizes a criterion. The difference is that the new criterion was designed to be insensitive to the outliers. PCS is supported by FastPCS, a fast and affine equivariant algorithm which we also detail. Both an extensive simulation study and a real data application from the field of engineering show that FastPCS performs better than its competitors.