Clustering for rotation-valued functional data

Aymeric Stamm
Laboratoire de Mathématiques Jean Leray - UMR CNRS, Nantes, France
Wednesday 26th April 2023
Politecnico di Milano, Dipartimento di Matematica (Edificio 14 - La Nave), Aula Saleri
This talk is motivated by the strong case study of monitoring gait for early detection of gait impairment in patients diagnosed with gait-affecting disorders. To this effect, we record the rotation of the hip over time. This leads to data with a great complexity that makes any kind of statistical analysis non-trivial. In effect, we collect functional data that evaluates on the Lie group of three-dimensional rotations which is a non-Euclidean space. In this work, we develop sound statistical methods to enable joint clustering and alignment of such functional data by borrowing ideas from the existing k-means alignment approach. In the process, we will describe in great length the R package fdacluster, which is an extension of the R package fdakma that provides a fast C++ based implementation of the k-mean alignment algorithm from Sangalli et al. (2010) as well as hierarchical clustering for functional data and tools that help choosing the number of clusters. Il link per seguire il seminario online sarà reso disponibile pochi minuti prima dell’avvio del seminario