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Clustering stands as one of the most prominent challenges in unsupervisedmachine learning. Among centroid-based methods, the classic $k$-meansalgorithm, based on Lloyd's heuristic, is widely used. Nonetheless, it is awell-known fact that $k$-means and its variants face several challenges,including heavy reliance on initial cluster centroids, susceptibility toconverging into local minima of the objective function, and sensitivity tooutliers and noise in the data. When data contains noise or outliers, theMedian-of-Means (MoM) estimator offers a robust alternative for stabilizingcentroid-based methods. On a different note, another limitation in manycommonly used clustering methods is the need to specify the number of clustersbeforehand. Model-based approaches, such as Bayesian nonparametric models,address this issue by incorporating infinite mixture models, which eliminatethe requirement for predefined cluster counts. Motivated by these facts, inthis article, we propose an efficient and automatic clustering technique byintegrating the strengths of model-based and centroid-based methodologies. Ourmethod mitigates the effect of noise on the quality of clustering; while at thesame time, estimates the number of clusters. Statistical guarantees on an upperbound of clustering error, and rigorous assessment through simulated and realdatasets, suggest the advantages of our proposed method over existingstate-of-the-art clustering algorithms.

Dirichlet Process-based Robust Clustering using the Median-of-Means Estimator