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This paper explores the issue of recognizing, generalizing and reproducing arbitrary gestures. We aim at extracting a representation that encapsulates only the key aspects of the gesture and discards the variability intrinsic to each person's motion. We compare a decomposition into principal components (PCA) and independent components (ICA) as a first step of preprocessing in order to decorrelate and denoise the data, as well as to reduce the dimensionality of the dataset to make this one tractable. In a second stage of processing, we explore the use of a probabilistic encoding through continuous Hidden Markov Models (HMMs), as a way to encapsulate the sequential nature and intrinsic variability of the motions in stochastic finite state automata. Finally, the method is validated in a humanoid robot to reproduce a variety of gestures performed by a human demonstrator.