Geometric description and characterization of time series signals

Abstract

This paper considers time series signals in Rn as samples of an embedded space curve and proceeds to characterize such signals in terms of differential-geometric descriptors of their associated curves. In particular, a method of estimating curvature as a function of arc length is presented. Because arc length is invariant to reparameterization of a space curve, this approach provides a representation of the evolution of the time series that is invariant to local variations in the rate of the time series as well as displacement and rotation of the curve in space. The focus here is on ascertaining structural similarity of time series signals by measuring similarity of their curvatures, though extension to other applications and other geometric descriptors (e.g., torsion) is envisioned.