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Real-time stream mining such as surveillance and personal health monitoring, which involves sophisticated mathematical operations, is computation-intensive and prohibitive for mobile devices due to the hardware/computation constraints. To satisfy the growing demand for stream mining in mobile networks, we propose to employ a cloud-based stream mining system in which the mobile devices send via wireless links unclassified media streams to the cloud for classification. We aim at minimizing the classification-energy cost, defined as an affine combination of classification cost and energy consumption at the cloud, subject to an average stream mining delay constraint (which is important in real-time applications). To address the challenge of time-varying wireless channel conditions without a priori information about the channel statistics, we develop an online algorithm in which the cloud operator can dynamically adjust its resource provisioning on the fly and the mobile devices can adapt their transmission rates to the instantaneous channel conditions. It is proved that, at the expense of increasing the average stream mining delay, the online algorithm achieves a classification-energy cost that can be pushed arbitrarily close to the minimum cost achieved by the optimal offline algorithm. Extensive simulations are conducted to validate the analysis.