Improved time series clustering based on new geometric frameworks. (April 2022) - Péalat, Clément; Bouleux, Guillaume; Cheutet, Vincent
Highlights: We use the geometrical information of the time series via Takens embedding. We analyze the geometrical information obtained by the embedding on the Stiefel, the unit sphere and the R n × p manifolds. We point out the gain obtained by such an embedding with respect to traditional time series clustering approaches. We analyze over 79 times series databases different frameworks. The advocated framework is the Stiefel embedding followed by the UMAP and HDBSCAN algorithms. Abstract: Most existing methods for time series clustering rely on distances calculated from the entire raw data using the Euclidean distance or Dynamic Time Warping distance. In this work, we propose to embed the time series onto higher-dimensional spaces to obtain geometric representations of the time series themselves. Particularly, the embedding on R n × p, on the Stiefel manifold and on the unit Sphere are analyzed for their performances with respect to several yet well-known clustering algorithms. The gain brought by the geometrical representation for the time series clustering is illustrated through a large benchmark of databases. We particularly exhibit that, firstly, the embedding of the time series on higher dimensional spaces gives better results than classical approaches and, secondly, that the embedding on the Stiefel manifold - in conjunction with UMAP and HDBSCAN clustering algorithms - is the recommended framework for time series clustering.