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

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 effectiveness of the pseudo-metric property and its centroid in capturing the ‘shape’ of a time series set, using two important machine learning techniques, namely: Nearest Centroid Classifier and K-Means clustering, using 85 publicly available data sets. Shape-Sphere improves the nearest centroid classification results when the shape is the differentiating feature while keeping the quality of clustering equivalent to current state-of-the-art techniques.