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Time series clustering is an essential ingredient of unsupervised learning techniques. It provides an understanding of the intrinsic properties of data upon exploiting similarity measures. Traditional similarity-based methods usually consider local geometric properties of raw time series or the global topological properties of time series in the phase space. In order to overcome their limitations, we put forward a time series clustering framework, referred to as time series clustering with Topological-Geometric Mixed Distance (TGMD), which jointly considers local geometric features and global topological characteristics of time series data. More specifically, persistent homology is employed to extract topological features of time series and to compute topological similarities among persistence diagrams. The geometric properties of raw time series are captured by using shape-based similarity measures such as Euclidean distance and dynamic time warping. The effectiveness of the proposed TGMD method is assessed by extensive experiments on synthetic noisy biological and real time series data. The results reveal that the proposed mixed distance-based similarity measure can lead to promising results and that it performs better than standard time series analysis techniques that consider only topological or geometrical similarity.

Time Series Clustering with Topological and Geometric Mixed Distance