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.

中文翻译：

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用于从有限位置的聚合数据推断潜在人员流的时延集体流扩散模型

摘要 无线传感器设备的快速普及使得记录各种空间（例如展厅）中人员的位置信息变得更加容易。由于隐私和/或成本问题，位置信息经常被汇总。我们用作输入的汇总数据包括每个位置和每个时间步的进出人数。由于聚合数据缺乏个人的跟踪信息，因此确定地点之间的人流并不简单。在本文中，我们解决了从观察位置收集的汇总人口数据推断潜在人口流动的问题，即位置之间的过渡人口。现有模型假设每个人在每个时间步都始终处于观察到的位置之一；然而，这是一个不切实际的假设，因为我们并不总是有足够多的传感器设备来覆盖目标的大规模空间。为了克服这个缺点，我们提出了一种具有流量守恒约束的概率模型，该模型结合了观察位置之间的旅行持续时间分布。为了处理嘈杂的设置，我们对进出的人数采用了噪声观测模型，其中噪声被视为可能干扰流量守恒的因素，例如，人们可能会出现在预定的感兴趣空间中或从其消失。我们开发了一种近似的期望最大化 (EM) 算法，该算法可以同时估计过渡种群和模型参数。我们的实验证明了所提出的模型对展厅行人数据的真实世界数据集的有效性，