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、群体范围内的行为，或者包括更多的细节层次，直到个体被跟踪的微观描述。该项目的一项主要任务是在人口水平的平均流动流量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，以建立人口平均流量的模型。另一方面，一旦这个模型建立起来，它允许我们分类观察到的模式有多罕见，在这种模式中，几个被认为是独立的个体以非常协调的方式行事。这个项目包括在全球移民模式模型和一小部分移民的行为之间进行类似的匹配。除了异常检测之外，预测机动性也很重要。一旦从观测数据中推断出流动性模型，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，并发现脆弱性，无论是城市交通还是全球移民。这个项目在两个细节层面上处理人类动态的概率描述：种群平均时间进化的确定性描述，以及个体轨迹随机结果的描述。关于马尔可夫半群扰动的费曼-卡茨公式的一个版本是连接两个层次的概率描述的中心元素。从样本轨迹中建立模型的技术是图信号处理新兴领域的新发展，结合了统计学和动力系统的元素。在群体平均和个体水平上的动力学行为都由发电机来表征。它对观察事件的概率进行编码，并允许我们预测流量或计算观察轨迹与最可能轨迹之间的可能性比，从而允许对个人行为进行分类。本项目处理的一个主要问题是对不同尺度模型的人口流动产生因素进行准确估计。然后用这个估计来预测机动性或检测小组单个轨迹中的异常。本项目考虑的流动模式包括迁移、全球人口在不同国家间流动的时间演变，或较小规模的流动，例如，通过观察个人的GPS轨迹或城市交通系统获取的数据推断交通流量。这个项目研究在哪些额外的、正则化的假设下可以对发电机进行可靠的估计。在这种情况下，可以用期望的似然比水平检测到移动模式中的异常。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。该项目的结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人类移动性的模型。该奖项反映了美国国家科学基金会的法定使命，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.