New paper on smoothing methods for rotation-valued functional data

Check out our newly published research which compares smoothing methods for functional representation of rotation-valued time series when the scope is to perform classification tasks.

rotation-valued functional data
data representation

Department of Mathematics Jean Leray, UMR CNRS 6629


June 9, 2023

Smoothing orientation data is a fundamental task in different fields of research. Different methods of smoothing time series in quaternion algebras have been described in the literature, but their application is still an open point. This paper develops a smoothing approach for smoothing quaternion time series to obtain good performance in classification problems. Starting from an existing method which involves an angular velocity transformation of unit quaternion time series, a new method which employ the logarithm function to transform the quaternion time series to a real three-dimensional time series is proposed. Empirical evidences achieved on real data set and artificially noisy data sets confirm the effectiveness of the proposed method compared with the classical approach based on angular velocity transformation. The R functions developed for this paper will be provided in a Github repository.

Find out more by reading our paper (Ballante et al. 2023) which can be found at


Ballante, Elena, Lise Bellanger, Pierre Drouin, Silvia Figini, and Aymeric Stamm. 2023. “Smoothing Method for Unit Quaternion Time Series in a Classification Problem: An Application to Motion Data.” Scientific Reports 13 (1): 9366.