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Odor classification by a robot equipped with an electronic nose (e-nose) is a challenging task for pattern recognition since volatiles have to be classified quickly and reliably even in the case of short measurement sequences, gathered under operation in the field. Signals obtained in these circumstances are characterized by a high-dimensionality, which limits the use of classical classification techniques based on unsupervised and semi-supervised settings, and where predictive variables can be only identified using wrapper or post-processing techniques. In this paper, we consider generative topographic mapping through time (GTM-TT) as an unsupervised model for time-series inspection, based on hidden Markov models regularized by topographic constraints. We further extend the model such that supervised classification and relevance learning can be integrated, resulting in supervised GTM-TT. Then, we evaluate the suitability of this new technique for the odor classification problem in robotics applications. The performance is compared with classical techniques as nearest neighbor, as an absolute baseline, support vector machine and a recent time-series kernel approach, demonstrating the eligibility of our approach for high-dimensional data. Additionally, we exploit the learning system introduced in this work, providing a measure of the relevance of each sensor and individual time points in the classification process, from which important information can be extracted. [ABSTRACT FROM AUTHOR]