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Classifiers trained on data sets possessing an imbalanced class distribution are known to exhibit poor generalisation performance. This is known as the imbalanced learning problem. The problem becomes particularly acute when we consider incremental classifiers operating on imbalanced data streams, especially when the learning objective is rare class identification. As accuracy may provide a misleading impression of performance on imbalanced data, existing stream classifiers based on accuracy can suffer poor minority class performance on imbalanced streams, with the result being low minority class recall rates. In this paper we address this deficiency by proposing the use of the Hellinger distance measure, as a very fast decision tree split criterion. We demonstrate that by using Hellinger a statistically significant improvement in recall rates on imbalanced data streams can be achieved, with an acceptable increase in the false positive rate.