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...However noisy values commonly exist in high-speed data streams, e.g. real-time online data feeds that are prone to interference. When processing big data, it is hard to implement pre-processing and sampling in full batches. To solve this trade-off, we propose a new decision tree so called incrementally optimized very fast decision tree (iOVFDT). Inheriting the use of Hoeffding bound in VFDT algorithm for node-splitting check, it contains four optional strategies of functional tree leaf, which improve the classifying accuracy. In addition, a multi-objective incremental optimization mechanism investigates a balance among accuracy, mode size and learning speed...