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Clustering algorithms do not learn, but they can be learned

Pattern classification theory involves an error criterion, optimal classifiers, and a theory of learning. For clustering, there has historically been little theory; in particular, there has generally (but not always) been no learning. The key point is that clustering has not been grounded on a probabilistic theory. Recently, a clustering theory has been developed in the context of random sets. This paper discusses learning within that context, in particular, k- nearest-neighbor learning of clustering algorithms.