Predicting time series necessitates choosing adequate regressors. For this purpose, prior knowledge of the data is required. By projecting the series on a low-dimensional space, the visualization of the regressors helps to extract relevant information. However, when the series includes some periodicity, the structure of the time series is better projected on a sphere than on an Euclidean space. This paper shows how to project time series regressors on a sphere. A user defined parameter is introduced in a pairwise distance criterion to control the trade-off between trustworthiness and continuity. Moreover, the theory of optimization on manifolds is used to minimize this criterion on a sphere.
Onclinx, V., Verleysen, M., & Wertz, V. (2008). Projection of time series with periodicity on a sphere. Proceedings of the European Symposium on Time Series Prediction (ESTSP′08), p. 47-56. https://hdl.handle.net/2078.5/254177