Bidirectional Piecewise Linear Representation of Time Series and Its Application in Clustering

The high dimensionality of time series data presents challenges for direct mining, including time and computational resource costs. In this study, a novel data representation method for time series is proposed and validated in a hierarchical clustering task. Firstly, the bidirectional segmentation algorithm, called BPLR, is introduced for piecewise linear representation. Through this method, the original time series is transformed into a set of linear fitting functions, thereby producing a concise, lower-dimensional linear fitting (LF) time series that encapsulates the original data. Next, based on dynamic time warping (DTW) distance, a new similarity measure is proposed to compute the distance between any two LF time series, which is called LF-DTW distance. The proposed LF-DTW distance exhibits good performance in handling time-scale distortions between time series. Finally, hierarchical clustering is realized based on the proposed LF-DTW distance. The efficiency and advantages of the proposed approach are validated through experimental results using real-world data. Owing to its ability to capture the inherent structure of time series, the proposed approach consistently outperforms methods based on classic distance metrics and other existing clustering algorithms