Decentralized Trajectory Tracking Using Homology and Hodge Decomposition in Sensor Networks

TL;DR

This paper introduces a decentralized topological method for classifying human movement trajectories in sensor networks, leveraging homology and Hodge decomposition to enable real-time, low-communication classification in complex environments.

Contribution

It presents a novel decentralized approach using topological representations and Hodge decomposition for efficient trajectory classification in sensor networks.

Findings

Effective classification of simulated museum trajectories.

Successful differentiation of real-world taxi trajectories.

Supports real-time processing with minimal communication.

Abstract

With the recent development of localization and tracking systems for both indoor and outdoor settings, we consider the problem of sensing, representing and analyzing human movement trajectories that we expect to gather in the near future. In this paper, we propose to use the topological representation, which records how a target moves around the natural obstacles in the underlying environment. We demonstrate that the topological information can be sufficiently descriptive for many applications and efficient enough for storing, comparing and classifying these natural human trajectories. We pre-process the sensor network with a purely decentralized algorithm such that certain edges are given numerical weights. Then we can perform trajectory classification by simply summing up the edge weights along the trajectory. Our method supports real-time classification of trajectories 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.