An Impartial Trimming Approach for Joint Dimension and Sample Reduction

A robust version of reduced and factorial k-means is proposed that is based on the idea of trimming. Reduced and factorial k-means are data reduction techniques well suited for simultaneous dimension and sample reduction through PCA and clustering. The occurrence of data inadequacies can invalidate standard analyses. Actually, contamination in the data at hand can hide the underlying clustered structure of the data. An appealing approach to develop robust counterparts of factorial and reduced k-means is given by impartial trimming. The idea is to discard a fraction of observations that are selected as the most distant from the centroids. The finite sample behavior of the proposed methods has been investigated by some numerical studies and real data examples.