Decentralized human trajectories tracking using hodge decomposition in sensor networks

With the recent development of localization and tracking systems for both indoor and outdoor settings, we consider the problem of analyzing and representing the huge amount of natural trajectories from human movements that we expect to gather in the near future. In this paper we argue the topological representation, which records how a target moves around the natural obstacles in the underlying environment, can be sufficiently descriptive for many applications and efficient enough for both storing, comparing and classifying these natural human trajectories. Technically, the representation uses the homotopy type of the trajectory. By using harmonic oneforms and Hodge decomposition, we pre-process the sensor network with a purely decentralized algorithm such that the homology class of a trajectory can be obtained by a simple integration along the trajectory. This supports real-time classification of trajectories up to the homology accuracy with minimum communication cost. We test the effectiveness of our approach by showing how to classify randomly generated trajectories in a multi-level arts museum layout as well as how to distinguish real world taxi trajectories in a large city.