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. First, the bidirectional segmentation algorithm, called BPLR, is introduced for piecewise linear representation (PLR). Through this method, the original time series is transformed into a set of linear fitting (LF) functions, thereby producing a concise, lower-dimensional 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.