Improved time series clustering based on new geometric frameworks

•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 Rn×p manifolds.•We point out the gain obtained by such an embedding with respect to traditional time series clustering...

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Veröffentlicht in:Pattern recognition Jg. 124; S. 108423
Hauptverfasser: Péalat, Clément, Bouleux, Guillaume, Cheutet, Vincent
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.04.2022
Elsevier
Schlagworte:
Clustering
Computer Aided Engineering
Computer Science
Delayed coordinate embedding
Embedding
Engineering Sciences
HDBSCAN
Mechanical engineering
Mechanics
Stiefel manifold
Time series
UMAP
UMAP
HDBSCAN
Stiefel manifold
Time series
Embedding
Clustering
Delayed coordinate embedding
Stiefel Manifold
ISSN:0031-3203, 1873-5142
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Zusammenfassung:•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 Rn×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. 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 Rn×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.
ISSN:0031-3203
1873-5142
DOI:10.1016/j.patcog.2021.108423