Time series ordinal classification via shapelets

Nominal time series classification has been widely developed over the last years. However, to the best of our knowledge, ordinal classification of time series is an unexplored field, and this paper proposes a first approach in the context of the shapelet transform (ST). For those time series dataset where there is a natural order between the labels and the number of classes is higher than 2, nominal classifiers are not capable of achieving the best results, because the models impose the same cost of misclassification to all the errors, regardless the difference between the predicted and the ground-truth. In this sense, we consider four different evaluation metrics to do so, three of them of an ordinal nature. The first one is the widely known Information Gain (IG), proved to be very competitive for ST methods, whereas the remaining three measures try to boost the order information by refining the quality measure. These three measures are a reformulation of the Fisher score, the Spearman's correlation coefficient (ρ), and finally, the Pearson's correlation coefficient (R
²
). An empirical evaluation is carried out, considering 7 ordinal datasets from the UEA & UCR time series classification repository, 4 classifiers (2 of them of nominal nature, whereas the other 2 are of ordinal nature) and 2 performance measures (correct classification rate, CCR, and average mean absolute error, AMAE). The results show that, for both performance metrics, the ST quality metric based on R
²
is able to obtain the best results, specially for AMAE, for which the differences are statistically significant in favour of R
²
.