Trimmed $k$-means: an attempt to robustify quantizers

Abstract

A class of procedures based on "impartial trimming" (self-determined by the data) is introduced with the aim of robustifying k-means, hence the associated clustering analysis. We include a detailed study of optimal regions, showing that only nonpathological regions can arise from impartial trimming procedures. The asymptotic results provided in the paper focus on strong consistency of the suggested methods under widely general conditions. A section is devoted to exploring the performance of the procedure to detect anomalous data in simulated data sets.