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Centroid based clustering methods such as k-means, k-medoids and k-centersare heavily applied as a go-to tool in exploratory data analysis. In manycases, those methods are used to obtain representative centroids of the datamanifold for visualization or summarization of a dataset. Real world datasetsoften contain inherent abnormalities, e.g., repeated samples and sampling bias,that manifest imbalanced clustering. We propose to remedy such a scenario byintroducing a maximal radius constraint $r$ on the clusters formed by thecentroids, i.e., samples from the same cluster should not be more than $2r$apart in terms of $\ell_2$ distance. We achieve this constraint by solving asemi-definite program, followed by a linear assignment problem with quadraticconstraints. Through qualitative results, we show that our proposed method isrobust towards dataset imbalances and sampling artifacts. To the best of ourknowledge, ours is the first constrained k-means clustering method with hardradius constraints. Codes at https://bit.ly/kmeans-constrained

No More Than 6ft Apart: Robust K-Means via Radius Upper Bounds