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Clustering spatially distributed data is well motivated and especially challenging when communication to a central processing unit is discouraged, e.g., due to power constraints. Distributed clustering schemes are developed in this paper for both deterministic and probabilistic approaches to unsupervised learning. The centralized problem is solved in a distributed fashion by recasting it to a set of smaller local clustering problems with consensus constraints on the cluster parameters. The resulting iterative schemes do not exchange local data among nodes, and rely only on single-hop communications. Performance of the novel algorithms is illustrated with simulated tests on synthetic and real sensor data. Surprisingly, these tests reveal that the distributed algorithms can exhibit improved robustness to initialization than their centralized counterparts.