TY - GEN

T1 - Ordering Principal Components of Multivariate Fractional Brownian Motion for Solving Inverse Problems.

AU - Mohr, Marisa

AU - Möller, Ralf

N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2021

Y1 - 2021

N2 - The problem of recovering information about a generating time-dependent dynamical system from measurement data is investigated as an inverse problem. Fractional Brownian motion is often used for modelling real-world applications that deal with specific properties such as long-range dependence or self-similarity. The self-similarity parameter, also known as Hurst parameter H, is directly related to the distribution of ordinal patterns in fractional Brownian motion. Thus the corresponding information entropy measure, known as permutation entropy, can extract significant information about the generating system. As real-world applications often involve multivariate correlated measurements, multivariate variants of permutation entropy have to be considered. While pooled permutation entropy is able to estimate H, it fails to detect cross-correlations between variables. In this work, we use multivariate permutation entropy based on principal component analysis (MPE-PCA) to investigate self-similarity and cross-correlations. We examine the variation of permutation entropy of principal components with variations of H and cross-correlations and find those principal components behave equally to their origin under certain conditions, i.e., as H increases, the MPE-PCA of the principal components decreases. Furthermore, MPE-PCA discovers cross-correlations in multivariate fractional Brownian motion.

AB - The problem of recovering information about a generating time-dependent dynamical system from measurement data is investigated as an inverse problem. Fractional Brownian motion is often used for modelling real-world applications that deal with specific properties such as long-range dependence or self-similarity. The self-similarity parameter, also known as Hurst parameter H, is directly related to the distribution of ordinal patterns in fractional Brownian motion. Thus the corresponding information entropy measure, known as permutation entropy, can extract significant information about the generating system. As real-world applications often involve multivariate correlated measurements, multivariate variants of permutation entropy have to be considered. While pooled permutation entropy is able to estimate H, it fails to detect cross-correlations between variables. In this work, we use multivariate permutation entropy based on principal component analysis (MPE-PCA) to investigate self-similarity and cross-correlations. We examine the variation of permutation entropy of principal components with variations of H and cross-correlations and find those principal components behave equally to their origin under certain conditions, i.e., as H increases, the MPE-PCA of the principal components decreases. Furthermore, MPE-PCA discovers cross-correlations in multivariate fractional Brownian motion.

M3 - Conference contribution

SP - 240

EP - 247

BT - APSIPA ASC

ER -