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Mathematics > Rings and Algebras

arXiv:1906.05823 (math)
[Submitted on 13 Jun 2019 (v1), last revised 11 Mar 2020 (this version, v2)]

Title:Time-warping invariants of multidimensional time series

Authors:Joscha Diehl, Kurusch Ebrahimi-Fard, Nikolas Tapia
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Abstract:In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, as a first step, features of the time series need to be extracted. These are numerical quantities that aim to succinctly describe the data and to dampen the influence of noise. In some applications, these features are also required to satisfy some invariance properties. In this paper, we concentrate on time-warping invariants. We show that these correspond to a certain family of iterated sums of the increments of the time series, known as quasisymmetric functions in the mathematics literature. We present these invariant features in an algebraic framework, and we develop some of their basic properties.
Comments: 18 pages, 1 figure
Subjects: Rings and Algebras (math.RA); Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG)
MSC classes: 60L10, 16T05, 62M10, 68T10
Cite as: arXiv:1906.05823 [math.RA]
  (or arXiv:1906.05823v2 [math.RA] for this version)
  https://doi.org/10.48550/arXiv.1906.05823
Journal reference: Acta Applicandae Mathematicae 170(1) (2020), 265--290
Related DOI: https://doi.org/10.1007/s10440-020-00333-x

Submission history

From: Nikolas Tapia [view email]
[v1] Thu, 13 Jun 2019 17:09:19 UTC (75 KB)
[v2] Wed, 11 Mar 2020 10:55:59 UTC (48 KB)
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