Is Medoid Suitable for Averaging GPS Trajectories?

Abstract

Averaging GPS trajectories is needed in applications such as clustering and automatic extraction of road segments. Calculating mean for trajectories and other time series data is non-trivial and shown to be an NP-hard problem. medoid has therefore been widely used as a practical alternative and because of its (assumed) better noise tolerance. In this paper, we study the usefulness of the medoid to solve the averaging problem with ten different trajectory-similarity/-distance measures. Our results show that the accuracy of medoid depends mainly on the sample size. Compared to other averaging methods, the performance deteriorates especially when there are only few samples from which the medoid must be selected. Another weakness is that medoid inherits properties such as the sample frequency of the arbitrarily selected sample. The choice of the trajectory distance function becomes less significant. For practical applications, other averaging methods than medoid seem a better alternative for higher accuracy.