Dynamic time warping similarity measurement based on low-rank sparse representation

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.