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One versus all (OVA) decision trees learn k individual binary classifiers, each one to distinguish the instances of a single class from the instances of all other classes. Thus OVA is different from existing data stream classification schemes whose majority use multiclass classifiers, each one to discriminate among all the classes. This paper advocates some outstanding advantages of OVA for data stream classification. First, there is low error correlation and hence high diversity among OVA's component classifiers, which leads to high classification accuracy. Second, OVA is adept at accommodating new class labels that often appear in data streams. However, there also remain many challenges to deploy traditional OVA for classifying data streams. First, as every instance is fed to all component classifiers, OVA is known as an inefficient model. Second, OVA's classification accuracy is adversely affected by the imbalanced class distribution in data streams. This paper addresses those key challenges and consequently proposes a new OVA scheme that is adapted for data stream classification. Theoretical analysis and empirical evidence reveal that the adapted OVA can offer faster training, faster updating and higher classification accuracy than many existing popular data stream classification algorithms.