Snipping for robust k-means clustering under component-wise contamination

Abstract

We introduce the concept of snipping, complementing that of trimming, in robust cluster analysis. An observation is snipped when some of its dimensions are discarded, but the remaining are used for clustering and estimation. Snipped k-means is performed through a probabilistic optimization algorithm which is guaranteed to converge to the global optimum. We show global robustness properties of our snipped k-means procedure. Simulations and a real data application to optical recognition of handwritten digits are used to illustrate and compare the approach.