High Dimensional Time Series Generators

Abstract: Multidimensional time series are sequences of real valued vectors. They occur in different areas, for example handwritten characters, GPS tracking, and gestures of modern virtual reality motion controllers. Within these areas, a common task is to search for similar time series. Dynamic Time Warping (DTW) is a common distance function to compare two time series. The Edit Distance with Real Penalty (ERP) and the Dog Keeper Distance (DK) are two more distance functions on time series. Their behaviour has been analyzed on 1-dimensional time series. However, it is not easy to evaluate their behaviour in relation to growing dimensionality. For this reason we propose two new data synthesizers generating multidimensional time series. The first synthesizer extends the well known cylinder-bell-funnel (CBF) dataset to multidimensional time series. Here, each time series has an arbitrary type (cylinder, bell, or funnel) in each dimension, thus for $d$-dimensional time series there are $3^{d}$ different classes. The second synthesizer (RAM) creates time series with ideas adapted from Brownian motions which is a common model of movement in physics. Finally, we evaluate the applicability of a 1-nearest neighbor classifier using DTW on datasets generated by our synthesizers.