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In this paper, we introduce a novel nonparametric classification technique based on the use of the Wasserstein distance. The proposed scheme is applied in a biomedical context for the analysis of recorded accelerometer data: the aim is to retrieve three types of periodic activities (walking, biking, and running) from a time-frequency representation of the data. The main interest of the use of the Wasserstein distance lies in the fact that it is less sensitive to the location of the frequency peaks than to the global structure of the frequency pattern, allowing us to detect activities almost independently of their speed or incline. Our system is tested on a 24-subject corpus: results show that the use of Wasserstein distance combined with some supervised learning techniques allows us to compare with some more complex classification systems.