ATD: Pop-Flow: Spatio-Temporal Modeling of Flows in Mobility Networks for Prediction and Anomaly Detection

人类流动可以在不同的尺度上进行建模，从城市交通到全球移民模式。这样的模型可以描述宏观的、群体范围的行为，或者包括更多层次的细节，直到个体被跟踪的微观描述。该项目的一个主要任务是在人口水平的平均流动流和观察到的个人轨迹之间进行转换。例如，从交通系统的记录中提取城市中通勤者和其他交通参与者的习惯，以便为人口平均流量建立模型。另一方面，一旦这个模型建立起来，它使我们能够对观察到的模式进行分类，即少数被认为是独立的个体以非常协调的方式行事的模式是多么罕见。该项目包括一个类似的全球移民模式和一小群移民行为之间的匹配。除了异常检测，预测移动性也很重要。一旦从观察到的数据中推断出移动模型，它就允许我们计算未来的事件，包括检测高流量区域。这有助于确定对基础设施的预期压力，并找到脆弱性，无论是城市交通还是全球移民。该项目将人类动力学的概率描述分为两个细节层次：人口平均时间演变的确定性描述，以及个人轨迹的随机结果描述。马尔可夫半群扰动的费曼-卡茨公式的一个版本是连接概率描述的两个层次的中心元素。所提出的从样本轨迹建模的技术是图形信号处理新兴领域的新发展，以及统计和动力系统的元素。在群体平均和个体水平上的动力学行为由生成器表征。它对观察事件的概率进行编码，并允许我们预测流或计算观察到的轨迹与最可能的轨迹之间的似然比，这允许对个体的行为进行分类。在这个项目中解决的一个主要问题是获得一个准确的估计，在不同尺度的模型的人口流动的发电机。然后，该估计用于预测移动性或检测小的个体轨迹集合中的异常。本项目考虑的流动模式包括移徙、成员在国家之间流动的全球人口的时间演变，或较小规模的流动，例如通过全球定位系统轨迹或城市交通系统获得的数据观察个人来推断交通流量。本项目调查在哪些额外的，正规化的假设下，可以对发电机进行可靠的估计。在这种情况下，可以利用期望的似然比水平来检测移动性模式中的异常。正则化包括最优运输计划和应用于图上信号的时频分析技术。该项目的成果将通过提供性能保证和严格的误差估计来补充工程文献中的人类流动模型。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Human mobility can be modeled at different scales, ranging from traffic in a city to global migration patterns. Such models can describe a macroscopic, population-wide behavior or include more levels of detail up to a microscopic description in which individuals are followed. A main task in this project is to convert between the averaged mobility flows at the population level and observed individual trajectories. For example, the habits of commuters and other traffic participants in a city are extracted from records of transportation systems in order to build a model for the population-averaged flow. On the other hand, once this model is established, it permits us to classify how rare an observed pattern is in which a few individuals that were assumed to be independent behave in a very coordinated way. This project includes a similar matching between a model for global migration patterns and the behavior of a small group of migrants. Next to anomaly detection, predicting mobility is important. Once the mobility model is inferred from the observed data, it permits us to compute future events, including the detection of high-traffic areas. This helps determine an expected stress on infrastructure and find vulnerabilities, whether it is for urban traffic or global migration.This project treats the probabilistic description of human dynamics at two levels of detail: The deterministic description of the population-averaged time evolution, and the description of the random outcomes for individual trajectories. A version of the Feynman-Kac formula for perturbations of Markov semigroups is the central element that connects the two levels of the probabilistic description. The proposed techniques for model building from sample trajectories are new developments in the emergent field of graph signal processing, together with elements of statistics and dynamical systems. The behavior of dynamics at both population-averaged and individual levels is characterized by the generator. It encodes the probabilities for observing an event and allows us to predict flows or to compute likelihood ratios between observed and most likely trajectories, which permits classifying the behavior of individuals. A main problem addressed in this project is to obtain an accurate estimate for the generator of population flows for models at different scales. This estimate is then used to predict mobility or to detect anomalies in small sets of individual trajectories. Mobility patterns considered in this project include migration, the time evolution of a global population whose members move between countries, or mobility at a smaller scale, for example the inference of traffic flows from observing individuals through GPS traces or data acquired by transportation systems in a city. This project investigates under which additional, regularizing assumptions reliable estimates of the generator can be made. In that case, anomalies in mobility patterns can be detected with desired levels for likelihood ratios. The regularization includes optimal transport plans and techniques of time-frequency analysis applied to signals on graphs. The outcomes of this project will complement models for human mobility in the engineering literature by providing performance guarantees and rigorous error estimates.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.