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In this paper we address the problem of combining multiple clusterings without access to the underlying features of the data. This process is known in the literature as clustering ensembles, clustering aggregation, or consensus clustering. Consensus clustering yields a stable and robust final clustering that is in agreement with multiple clusterings. We find that an iterative EM-like method is remarkably effective for this problem. We present an iterative algorithm and its variations for finding clustering consensus. An extensive empirical study compares our proposed algorithms with eleven other consensus clustering methods on four data sets using three different clustering performance metrics. The experimental results show that the new ensemble clustering methods produce clusterings that are as good as, and often better than, these other methods.