Reviews: Robust k-means: a Theoretical Revisit

In this paper the author studied theoretic properties of the robust k-means (RKM) formulation proposed in [5,23]. They first studied the robustness property, showing that if the f_\lambda function is convex, the one outlier is sufficient to break down the algorithm; and if f_\lambda need not be convex, then two outliers can breakdown the algorithm. On the other hand, under some structural assumptions on the non-outliers, then a non-trivial breakdown point can be established for RKM. The authors then study the consistency issue, generalising consistency results that are known for convex f_lambda to non convex f_\lambda. My main concern of the paper is that the results appear very specific and I am not entirely sure whether they will appeal to a more general audience in machine learning.