A Review of Multivariate Ordinal Pattern Representations

Abstract:

In real-world applications, one often deals with multivariate time series, e.g., with medical measurements, which are stored as ECG data are usually not determined from a single electrode but from multiple electrodes. Since ordinal pattern representations are designed for univariate time series, the concept has to be extended to the multivariate case in order to apply it for multivariate time series as well. Numerous studies introduce multivariate extensions of permutation entropy under the generic name “Multivariate Permutation Entropy”, which claim to be the general approach, although there are many differences between them with different strengths and weaknesses. In this talk, by multivariate permutation entropy (MPE) we denote the class of all multivariate extensions of permutation entropy. We divide them into four strategies. The first three are based on the concept of univariate ordinal patterns, while the fourth strategy is based on a new concept of multivariate ordinal patterns. We elaborate on the different characteristics of the strategies and discuss their possible applications.

The workshop is about bringing together researchers from different disciplines to address the different directions the permutation entropy has taken since first published as seminal paper of C. Bandt and B. Pompe 20 years ago – taken under consideration new developments like ordinal statistics and ordinal methods in machine learning.