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Data collection is a fundamental task in wireless sensor networks. In many applications of wireless sensor networks, approximate data collection is a wise choice due to the constraints in communication bandwidth and energy budget. In this paper, we focus on efficient approximate data collection with prespecified error bounds in wireless sensor networks. The key idea of our data collection approach ADC (Approximate Data Collection) is to divide a sensor network into clusters, discover local data correlations on each cluster head, and perform global approximate data collection on the sink node according to model parameters uploaded by cluster heads. Specifically, we propose a local estimation model to approximate the readings of sensor nodes in subsets, and prove rated error-bounds of data collection using this model. In the process of model-based data collection, we formulate the problem of selecting the minimum subset of sensor nodes into a minimum dominating set problem which is known to be NP-hard, and propose a greedy heuristic algorithm to find an approximate solution. We further propose a monitoring algorithm to adaptively adjust the composition of node subsets according to changes of sensor readings. Our trace-driven simulations demonstrate that ADC remarkably reduces communication cost of data collection with guaranteed error bounds.