Pseudometrics for time series classification by nearest neighbor

Despite the success of its applications in many areas, the dynamic time warping (DTW) distance does not satisfy the triangle inequality (subadditivity). Once we have a subadditive distance measure for time series, the measure will have at least one significant advantage over DTW; one can directly plug such distance measure into systems which exploit the subadditivity to perform faster similarity search techniques. We propose two frameworks for designing subadditive distance measures and a few examples of distance measures resulting from the frameworks. One framework is more general than the other and can be used to tailor distances from the other framework to gain better classification performance. Experimental results of nearest neighbor classification showed that the designed distance measures are practical for time series classification.