We present a clustering algorithm for use when the number of clusters is unknown. We first show that the EM algorithm for mixture modeling can be considered as an alternating minimization between the data space and the model space. We then show how data cleaning can be performed by alternating between the data space and two model spaces. Finally, we develop a mixture model approach that iteratively refines the model spaces, beginning with a coarse model and selecting finer models as indicated by the consistent Akaike information criterion
