Journal article

Shape-Sphere: A metric space for analysing time series by their shape

Yousef Kowsar, Masud Moshtaghi, Eduardo Velloso, James C Bezdek, Lars Kulik, Christopher Leckie

INFORMATION SCIENCES | ELSEVIER SCIENCE INC | Published : 2022

Abstract

Shape analogy is a key technique in analyzing time series. That is, time series are compared by how much they look alike. This concept has been applied for many years in geometry. Notably, none of the current techniques describe a time series as a geometric curve that is expressed by its relative location and form in space. To fill this gap, we introduce Shape-Sphere, a vector space where time series are presented as points on the surface of a sphere. We prove a pseudo-metric property for distances in Shape-Sphere. We show how to describe the average shape of a time series set using the pseudo-metric property of Shape-Sphere by deriving a centroid from the set. We demonstrate the effectivene..

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Grants

Funding Acknowledgements

This research was supported by the use of the NeCTAR Research Cloud, a collaborative Australian research platform sup-ported by the National Collaborative Research Infrastructure Strategy. We would also like to acknowledge the publicly avail-able time series data set available athttp:// www.timeseriesclassification.com [5] .