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

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..