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Explainable AI (XAI) is an important developing area but remains relativelyunderstudied for clustering. We propose an explainable-by-design clusteringapproach that not only finds clusters but also exemplars to explain eachcluster. The use of exemplars for understanding is supported by theexemplar-based school of concept definition in psychology. We show that findinga small set of exemplars to explain even a single cluster is computationallyintractable; hence, the overall problem is challenging. We develop anapproximation algorithm that provides provable performance guarantees withrespect to clustering quality as well as the number of exemplars used. Thisbasic algorithm explains all the instances in every cluster whilst anotherapproximation algorithm uses a bounded number of exemplars to allow simplerexplanations and provably covers a large fraction of all the instances.Experimental results show that our work is useful in domains involvingdifficult to understand deep embeddings of images and text.

Explainable Clustering via Exemplars: Complexity and Efficient Approximation Algorithms