Time-delayed Collective Flow Diffusion Models for Inferring Latent People Flow from Aggregated Data at Limited Locations

Abstract The rapid adoption of wireless sensor devices has made it easier to record location information of people in a variety of spaces (e.g., exhibition halls). Location information is often aggregated due to privacy and/or cost concerns. The aggregated data we use as input consist of the numbers of incoming and outgoing people at each location and at each time step. Since the aggregated data lack tracking information of individuals, determining the flow of people between locations is not straightforward. In this article, we address the problem of inferring latent people flows, that is, transition populations between locations, from just aggregated population data gathered from observed locations. Existing models assume that everyone is always in one of the observed locations at every time step; this, however, is an unrealistic assumption, because we do not always have a large enough number of sensor devices to cover the large-scale spaces targeted. To overcome this drawback, we propose a probabilistic model with flow conservation constraints that incorporate travel duration distributions between observed locations. To handle noisy settings, we adopt noisy observation models for the numbers of incoming and outgoing people, where the noise is regarded as a factor that may disturb flow conservation, e.g., people may appear in or disappear from the predefined space of interest. We develop an approximate expectation-maximization (EM) algorithm that simultaneously estimates transition populations and model parameters. Our experiments demonstrate the effectiveness of the proposed model on real-world datasets of pedestrian data in exhibition halls, bike trip data and taxi trip data in New York City.