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For similarity-based clustering, we propose modeling the entries of a given similarity matrix as the inner products of the unknown cluster probabilities. To estimate the cluster probabilities from the given similarity matrix, we introduce a left-stochastic non-negative matrix factorization problem. A rotation-based algorithm is proposed for the matrix factorization. Conditions for unique matrix factorizations and clusterings are given, and an error bound is provided. The algorithm isdblp:journals/jmlr/AroraGKF13 fatcat:4xutprxsb5cbjana7allvwguti