Robustification of the k-means clustering problem and tailored decomposition methods: when more conservative means more accurate

Abstract k -means clustering is a classic method of unsupervised learning with the aim partitioning given number measurements into clusters. In many modern applications, however, this approach suffers from unstructured measurement errors because result then represents erroneous instead retrieving true underlying structure. We resolve issue by applying techniques robust optimization to hedge against in observed data. To end, we derive strictly and $$\Gamma $$ ? -robust counterparts problem. Since nominal problem already NP-hard, global approaches are often not feasible practice. As remedy, develop tailored alternating direction methods decomposing search space as well robustified problems quickly obtain points good quality. Our numerical results reveal an interesting feature: less conservative -approach clearly outperformed method. particular, able recover clusterings original data even if only observed.