New Approaches in Ordinal Pattern Representations for Multivariate Time Series

Many practical applications involve classification tasks on time series data, e.g., the diagnosis of cardiac insufficiency by evaluating the recordings of an electrocardiogram. Since most machine learning algorithms for classification are not capable of dealing with time series directly, mappings of time series to scalar values, also called representations, are applied before using these algorithms. Finding efficient mappings, which capture the characteristics of a time series is subject of the field of representation learning and especially valuable in cases of few data samples. Time series representations based on information theoretic entropies are a proven and well-established approach. Since this approach assumes a total ordering it is only directly applicable to univariate time series and thus rendering it difficult for many real-world applications dealing with multiple measurements at the same time. Some extensions were established which also cope with multivariate time series data, but none of the existing approaches take into account potential correlations between the movement of the variables. In this paper we propose two new approaches, considering the correlation between multiple variables, which outperform state-of-the-art algorithms on realworld data sets.