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    Interpretable Time Series Classification using Linear Models and Multi-resolution Multi-domain Symbolic Representations
    The time series classification literature has expanded rapidly over the last decade, with many new classification approaches published each year. Prior research has mostly focused on improving the accuracy and efficiency of classifiers, with interpretability being somewhat neglected. This aspect of classifiers has become critical for many application domains and the introduction of the EU GDPR legislation in 2018 is likely to further emphasize the importance of interpretable learning algorithms. Currently, state-of-the-art classification accuracy is achieved with very complex models based on large ensembles (COTE) or deep neural networks (FCN). These approaches are not efficient with regard to either time or space, are difficult to interpret and cannot be applied to variable-length time series, requiring pre-processing of the original series to a set fixed-length. In this paper we propose new time series classification algorithms to address these gaps. Our approach is based on symbolic representations of time series, efficient sequence mining algorithms and linear classification models. Our linear models are as accurate as deep learning models but are more efficient regarding running time and memory, can work with variable-length time series and can be interpreted by highlighting the discriminative symbolic features on the original time series. We advance the state-of-the-art in time series classification by proposing new algorithms built using the following three key ideas: (1) Multiple resolutions of symbolic representations: we combine symbolic representations obtained using different parameters, rather than one fixed representation (e.g., multiple SAX representations); (2) Multiple domain representations: we combine symbolic representations in time (e.g., SAX) and frequency (e.g., SFA) domains, to be more robust across problem types; (3) Efficient navigation in a huge symbolic-words space: we extend a symbolic sequence classifier (SEQL) to work with multiple symbolic representations and use its greedy feature selection strategy to effectively filter the best features for each representation. We show that our multi-resolution multi-domain linear classifier (mtSS-SEQL+LR) achieves a similar accuracy to the state-of-the-art COTE ensemble, and to recent deep learning methods (FCN, ResNet), but uses a fraction of the time and memory required by either COTE or deep models. To further analyse the interpretability of our classifier, we present a case study on a human motion dataset collected by the authors. We discuss the accuracy, efficiency and interpretability of our proposed algorithms and release all the results, source code and data to encourage reproducibility.
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