Similarity measurement of time series is one of the focus issues in time series analysis and mining. Morphology maintenance of time series is a better way for performing a similarity measurement, and phase space reconstruction has the advantage of analyzing the morphology of time series, whereas it is prone to generate high-dimensional data. Linear dimensionality reduction methods have difficulty preserving complete information of time series data. Manifold-based learning methods can better preserve the local characteristics of data. Low-rank representation (LRR) finds the lowest rank representation of all data and is capable of capturing the global structure of data. Therefore, in this paper, we propose a dynamic time warping similarity measurement method based on low-rank sparse representation (LRSE_DTW) to reduce the dimensionality of time series data. We learn the low-rank sparse representation of the phase space and then embed it into low-dimensional space to maintain the morphology of the phase space. DTW is used to measure the distance between discriminant information obtained from the l_2,1-norm constraint on the projection matrix. To confirm the effectiveness of LRSE_DTW, time series classification experiments are carried out on public UCR time series classification archive. The results show that LRSE_DTW is superior to several other state-of-the-art time series similarity measurement methods.

时间序列的相似性度量是时间序列分析和挖掘中的重点问题之一。时间序列的形态维护是执行相似度测量的更好方法，相空间重构具有分析时间序列形态的优势，但易于生成高维数据。线性降维方法难以保留时间序列数据的完整信息。基于流形的学习方法可以更好地保留数据的局部特征。低秩表示（LRR）查找所有数据的最低秩表示，并且能够捕获数据的全局结构。因此，在本文中，我们提出了一种基于低秩稀疏表示（LRSE_DTW）的动态时间规整相似度测量方法，以减少时间序列数据的维数。我们学习相空间的低阶稀疏表示，然后将其嵌入到低维空间中以保持相空间的形态。DTW用于测量从DTW获得的判别信息之间的距离。l对投影矩阵有_2,1-范数约束。为了确认LRSE_DTW的有效性，对公共UCR时间序列分类档案进行了时间序列分类实验。结果表明，LRSE_DTW优于其他几种最新的时间序列相似性测量方法。