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Distributed data clustering in sensor networks is receiving increasing attention with the development of network technology. A variety of algorithms for distributed data clustering have been proposed recently. However, most of these algorithms have trouble with either non-Gaussian shaped data clustering or model order selection problem. In order to address such two problems simultaneously, we propose a novel discriminative clustering algorithm with rigorous convergence analysis via normalized information measures and then extend it to a distributed one by borrowing consensus algorithms from the multi-agent consensus community. More specifically, we first select the normalized information distance (NID) between cluster data and cluster labels as the objective function, by minimizing which, a Minimum Normalized Information Distance-based (MNID) algorithm with capabilities of non-Gaussian data clustering and model selection is then proposed. Next, to further implement the MNID algorithm in a distributed manner, we employ some finite-time multi-agent consensus algorithms over the sensor networks to calculate the global model parameters, where only local intermediate variables are exchanged between one-hop neighbors. Both the centralized and the distributed MNID algorithms are proved to converge rigorously. Finally, the validity of the proposed algorithms is demonstrated through numerical tests on both synthetic and real data.