Abstract
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.
Highlights
The rapid development of information technology has made available a large number of time series generated in various fields
We have methods based on geometric similarity, which focus on the local relations at a given time in the raw time series
We propose a clustering framework for time series, referred to as time series clustering with Topological-Geometric Mixed Distance (TGMD)
Summary
The rapid development of information technology has made available a large number of time series generated in various fields. We have methods based on geometric similarity, which focus on the local relations at a given time in the raw time series. On many types of data, these methods yield satisfactory results [1] These methods are able to detect similarity in time and shape and to describe local geometric differences [9], they usually ignore the dynamic of the time series from a global perspective [10]. The topological features are extracted by persistence diagram from the point cloud obtained from delay embedding of the time series, whereas the geometric properties are the local correlations at a given time in the raw time series. We propose a TGMD measure for time series clustering analysis by combining the local geometric and global topological features of time series.
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