Robust k-means: a theoretical revisitRobust k-means: a theoretical revisit Πλήρης Δημοσίευση σε Συνέδριο Conference Full Paper 2018-10-262016enOver the last years, many variations of the quadratic k-means clustering procedure have been proposed, all aiming to robustify the performance of the algorithm in the presence of outliers. In general terms, two main approaches have been developed: one based on penalized regularization methods, and one based on trimming functions. In this work, we present a theoretical analysis of the robustness and consistency properties of a variant of the classical quadratic k-means algorithm, the robust k-means, which borrows ideas from outlier detection in regression. We show that two outliers in a dataset are enough to breakdown this clustering procedure. However, if we focus on "well-structured" datasets, then robust k-means can recover the underlying cluster structure in spite of the outliers. Finally, we show that, with slight modifications, the most general non-asymptotic results for consistency of quadratic k-means remain valid for this robust variant.http://creativecommons.org/licenses/by/4.0/2891-289930th Annual Conference on Neural Information Processing SystemsAdvances in Neural Information Processing Systems Georgogiannis Alexandros Γεωργογιαννης Αλεξανδρος Neural information processing systems foundation k-means clustering