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Many existing studies in data mining literature follow the batch learning setting, which suffers from low efficiency and poor scalability. To tackle these challenges, we investigate a unified online learning framework for the big data stream classification task. Different from the existing online data stream classification techniques, we propose a unified Sparse Online Classification (SOC) framework. Based on SOC, we derive a second-order online learning algorithm and a cost-sensitive sparse online learning algorithm, which could successfully handle online anomaly detection tasks with the extremely unbalanced class distribution. As the performance evaluation, we analyze the theoretical bounds of the proposed algorithms and conduct an extensive set of experiments. 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