Improved time series clustering based on new geometric frameworks

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.

Empirical Analysis of Fund Index Volatility Based on Conditional Heteroscedasticity Model

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