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In this paper, a computationally efficient framework, referred to as ensemble of subset online sequential extreme learning machine (ESOS-ELM), is proposed for class imbalance learning from a concept-drifting data stream. The proposed framework comprises a main ensemble representing short-term memory, an information storage module representing long-term memory and a change detection mechanism to promptly detect concept drifts. In the main ensemble of ESOS-ELM, each OS-ELM network is trained with a balanced subset of the data stream. Using ELM theory, a computationally efficient storage scheme is proposed to leverage the prior knowledge of recurring concepts. A distinctive feature of ESOS-ELM is that it can learn from new samples sequentially in both the chunk-by-chunk and one-by-one modes. ESOS-ELM can also be effectively applied to imbalanced data without concept drift. On most of the datasets used in our experiments, ESOS-ELM performs better than the state-of-the-art methods for both stationary and non-stationary environments.