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Blind Source Separation (BSS) for time-sensitive applications in the Internet of Things (IoT) results in a tradeoff between separation speed and accuracy. Data extraction has been widely employed recently to solve this problem. Although the introduction of current data extraction methods reduces the required time for separation, it is at the expense of separation quality. In this paper, we propose Adaptive extraction-based Independent Component Analysis (AeICA) to address these limitations. Specifically, the speed of separation is improved by using the extracted subset of the available data without affecting the overall separation accuracy, which we demonstrate through extensive numerical evaluations. In particular, AeICA reduces the total separation time by 50% to 75%, compared to the most remarkable related work.