Fast Sparse Dynamic Time Warping

Dynamic time warping (DTW) has been applied to a wide range of machine learning problems involving the comparison of time series. An important feature of such time series is that they can sometimes be sparse in the sense that the data takes zero value at many epochs. This corresponds for example to quiet periods in speech or to a lack of physical activity. However, employing conventional DTW for such sparse time series runs a full search ignoring the zero data. Sparse dynamic time warping (SDTW) was previously developed which yields the exact DTW solution while reducing the time complexity by the order of a suitably defined sparsity ratio. This paper focuses on the development and analysis of a fast approximate algorithm for dynamic time warping based on the SDTW framework. We call this fast sparse dynamic time warping (FSDTW). This study includes numerical experiments which compare the performance and complexity of FSDTW with DTW, SDTW and other algorithms that approximate DTW for sparse time series. It is shown that FSDTW reduces the time complexity relative to SDTW by the order of the sparsity ratio with negligible error relative to the exact DTW distance.