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In this work, we consider the recognition of dynamic gestures based on representative sub-segments of a gesture, which are denoted as most discriminating segments (MDSs). The automatic extraction and recognition of such small representative segments, rather than extracting and recognizing the full gestures themselves, allows for a more discriminative classifier. A MDS is a sub-segment of a gesture that is most dissimilar to all other gesture sub-segments. Gestures are classified using a MDSLCS algorithm, which recognizes the MDSs using a modified longest common subsequence (LCS) measure. The extraction of MDSs from a data stream uses adaptive window parameters, which are driven by the successive results of multiple calls to the LCS classifier. In a preprocessing stage, gestures that have large motion variations are replaced by several forms of lesser variation. We learn these forms by adaptive clustering of a training set of gestures, where we reemploy the LCS to determine similarity between gesture trajectories. The MDSLCS classifier achieved a gesture recognition rate of 92.6% when tested using a set of pre-cut free hand digit (0-9) gestures, while hidden Markov models (HMMs) achieved an accuracy of 89.5%. When the MDSLCS was tested against a set of streamed digit gestures, an accuracy of 89.6% was obtained. At present the HMMs method is considered the state-of-the-art method for classifying motion trajectories. The MDSLCS algorithm had a higher accuracy rate for pre-cut gestures, and is also more suitable for streamed gestures. MDSLCS provides a significant advantage over HMMs by not requiring data re-sampling during run-time and performing well with small training sets.