Nature-inspired approaches for distance metric learning in multivariate time series classification

The applicability of time series data mining in many different fields has motivated the scientific community to focus on the development of new methods towards improving the performance of the classifiers over this particular class of data. In this context the related literature has extensively shown that dynamic time warping is the similarity measure of choice when univariate time series are considered. However, possible statistical coupling among different dimensions make the generalization of this metric to the multivariate case all but obvious. This has ignited the interest of the community in new distance definitions capable of capturing such inter-dimension dependences. In this paper we propose a simple dynamic time warping based distance that finds the best weighted combination between the dependent - where multivariate time series are treated as whole - and independent approaches - where multivariate time series are just a collection of unrelated univariate time series - of the time series to be classified. A benchmark of four heuristic wrappers, namely, simulated annealing, particle swarm optimization, estimation of distribution algorithms and genetic algorithms are used to evolve the set of weighting coefficients towards maximizing the cross-validated predictive score of the classifiers. In this context one of the most recurring classifiers is nearest neighbor. This classifier is couple with a distance that as afore mentioned, in most cases, have been dynamic time warping. The performance of the proposed approach is validated over datasets widely utilized in the related literature, from which it is concluded that the obtained performance gains can be enlarged by properly decoupling the influence of each dimension in the definition of the dependent dynamic time warping distance.