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Hidden Markov models (HMMs) are powerful tools for modelling the generative and observational processes behind time series. For short sequences, the small amount of data can make unreliable the estimates returned by the EM algorithm, which is generally used to learn HMMs. To gain robustness in these cases, an imprecise version of the EM algorithm, achieving an interval-valued quantification of the model parameters can be considered instead. The bounds of the likelihood assigned to a particular sequence with respect to these intervals can be efficiently computed. Overall, this provides a time series classification algorithm. To classify a new sequence, the bounds of the likelihood associated to the HMMs learned from the supervised sequences are evaluated, and the returned class label is that of the highest-likelihood interval. If two or more of these intervals overlap and they are associated to different labels, the classifier returns multiple classes, this corresponding to a condition of partial indecision for the class of a particular sequence. An application to human action recognition shows the effectiveness of this approach in discriminating the hard-to-classify instances (those for which the classifier returns many classes) from the “easy” ones (those for which a single class, which mostly is the correct one, is returned). This suggests the opportunity of an application of the proposed approach as an useful preprocessing tool for other time series classifiers.
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