The Discriminative Power of Shape an Empirical Study in Time Series Matching.

Shape provides significant discriminating power in time series matching of visual or geometric data as required in many important applications in graphics and vision. The well established dynamic time warping (DTW) algorithm and its variants do this matching by determining a non-linear time mapping to minimise euclidean distances between corresponding time-warped points. However the shape of curves is not considered. In this paper, we present a new shape-aware algorithm which uses time and shape correspondence (TSC) at increasing levels of detail to define a similarity measure with an norm to aggregate the results, making it robust to noise and missing data. The norm is implicitly regularised using a shape-based error. Through extensive experiments we empirically show that our algorithm outperforms existing state of the art algorithms, works more effectively with high dimensional data, and handles noise and missing data better. We demonstrate its versatile applicability and comparative performance using a large in-house created gait data base, an action data base from Microsoft, exercise action data from a local company, a large public time series data base from University of California, Riverside and hand movement in quaternion stream data format.