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This paper presents GeoDMA , which processes the GPS data from multiple vehicles to detect anomalous driving maneuvers, such as rapid acceleration, sudden braking, and rapid swerving. First, an unsupervised deep auto-encoder is designed to learn a set of unique features from the normal historical GPS data of all drivers. We consider the temporal dependency of the driving data for individual drivers and the spatial correlation among different drivers. Second, to incorporate the peer dependency of drivers in local regions, we develop a geographical partitioning algorithm to partition a city into several sub-regions to do the driving anomaly detection. Specifically, we extend the vehicle-vehicle dependency to road-road dependency and formulate the geographical partitioning problem into an optimization problem. The objective of the optimization problem is to maximize the dependency of roads within each sub-region and minimize the dependency of roads between any two different sub-regions. Finally, we train a specific driving anomaly detection model for each sub-region and perform in-situ updating of these models by incremental training. We implement GeoDMA in Pytorch and evaluate its performance using a large real-world GPS trajectories. The experiment results demonstrate that GeoDMA achieves up to 8.5% higher detection accuracy than the baseline methods.