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We consider the correlated data gathering problem in machine-to-machine communications. The machines implement distributed source coding and transmit their gathered data to the data aggregator. The data aggregator has limited radio resources and thus only a subset of machines are selected for transmission. Missing data from nonselected machines are reconstructed at the aggregator by exploiting data correlation. We first propose a data distortion measure based on information loss to characterize the reconstruction, and derive its relationship with the traditional mean squared error distortion analytically. Then, we formulate the machine selection problem with the objective of minimizing the overall data distortion given some resource constraints. We decouple the problem into subproblems and solve them by the proposed algorithm based on the cross entropy method. Numerical results demonstrate improved …