AF: Medium: Collaborative Research: Algorithmic Foundations for Trajectory Collection Analysis

这个项目邀请了来自杜克大学和斯坦福大学的计算几何、优化和计算机视觉方面的专家来开发一个理论和算法框架，用于分析来自传感器或模拟的大量弹道数据。轨迹是从时间间隔到多维空间的函数，在描述任何随时间演变的系统时都会出现。如今，从数亿个传感器记录或推断出轨迹数据，从手机上的交通监控系统和GPS传感器，到监控系统或智能手机中嵌入的摄像头，野战士兵的头盔或医疗设备中的摄像头，以及科学实验和模拟，如生物学中的分子动力学计算。弹道数据分析算法可用于视频检索系统、活动识别、设施监测和监视、医疗调查、交通导航辅助工具、军事分析和部署工具、娱乐等。其中许多应用领域涉及国家安全领域以及更广泛的社会利益领域。该项目追求的是一种变革性的方法，将个人轨迹的几何形状与整个轨迹集合提供的关于其成员的信息相结合。重点是简单而快速的算法，这些算法随大小和维度的变化而扩展，可以处理数据中的不确定性，并适应噪声和非均匀抽样测量的流。研究人员与许多学科的应用科学家合作的长期记录，并将继续通过联合出版物和研究研讨会，也与几个工业合作伙伴合作，将他们的新研究转移到这些科学领域。这个项目将在很大程度上依赖研究生和本科生的参与。参与的本科生将通过指导项目、软件开发和实地研究来补充他们的教育。为该项目使用和获得的数据集将通过在线储存库提供给社区。开发的软件也将公之于众。理解弹道数据集，并从其中提取有意义的信息，需要许多计算挑战。部分问题与可用数据的巨大规模有关，这些数据正在不断增长，但也有其他几个。弹道数据集在质量、格式和时间支持方面受到不确定性和异质性的影响。同时，单个轨迹可能具有复杂的形状，即使是微小的细微差别也可能导致其语义上的巨大差异。因此，理解轨迹数据的主要压力在于需要捕获单个轨迹的精细细节，以及利用集合的智慧，即利用嵌入在大量轨迹集合中但在任何单个轨迹中缺失的信息。这种对集合智慧的强调是该项目的主要主题之一，并导致了计算几何、组合和数值优化以及计算机视觉中的许多重要问题。该项目的另一个主题是学习和利用轨迹数据中连续和离散的可变性模式。将开发确定性和概率表示法来总结轨迹集合，以捕捉它们之间的共性和差异，并将设计有效的算法来计算这些表示法。基于这些概要，将开发用于估计来自给定集合的轨迹、在集合的上下文中相互比较轨迹、以及响应于查询从集合检索轨迹的方法。轨迹收集还将用于推断有关环境和参与这些运动的移动实体的信息。

This project engages experts in computational geometry, optimization, and computer vision from Duke and Stanford to develop a theoretical and algorithmic framework for analyzing large collections of trajectory data from sensors or simulations. Trajectories are functions from a time interval to a multi-dimensional space that arise in the description of any system that evolves over time.Trajectory data is being recorded or inferred from hundreds of millions of sensors nowadays, from traffic monitoring systems and GPS sensors on cell phones to cameras in surveillance systems or those embedded in smart phones, in helmets of soldiers in the field, or in medical devices, as well as from scientific experiments and simulations, such as molecular dynamics computations in biology. Algorithms for trajectory-data analysis can lead to video retrieval systems, activity recognition, facility monitoring and surveillance, medical investigation, traffic navigation aids, military analysis and deployment tools, entertainment, and much more. Many of these application fields intersect areas of national security, as well as domains of broader societal benefit.This project pursues a transformational approach that combines the geometry of individual trajectories with the information that an entire collection of trajectories provides about its members. Emphasis is on simple and fast algorithms that scale well with size and dimension, can handle uncertainty in the data, and accommodate streams of noisy and non-uniformly sampled measurements.The investigators have a long track record of collaboration with applied scientists in many disciplines, and will continue to transfer their new research to these scientific fields through joint publications and research seminars, also in collaboration with several industrial partners. This project will heavily rely on the participation of graduate and undergraduate students. Participating undergraduates will supplement their education with directed projects, software development, and field studies. Data sets used and acquired for this project will be made available to the community through online repositories. Software developed will also be made publicly available.Understanding trajectory data sets, and extracting meaningful information from them, entails many computational challenges. Part of the problem has to do with the huge scale of the available data, which is constantly growing, but there are several others as well. Trajectory data sets are marred by sensing uncertainty and heterogeneity in their quality, format, and temporal support. At the same time, individual trajectories can have complex shapes, and even small nuances can make big differences in their semantics.A major tension in understanding trajectory data is thus between the need to capture the fine details of individual trajectories and the ability to exploit the wisdom of the collection, i.e., to take advantage of the information embedded in a large collection of trajectories but missing in any individual trajectory. This emphasis on the wisdom of the collection is one of the main themes of the project, and leads to a multitude of important problems in computational geometry, combinatorial and numerical optimization, and computer vision. Another theme of the project is to learn and exploit both continuous and discrete modes of variability in trajectory data.Deterministic and probabilistic representations will be developed to summarize collections of trajectories that capture commonalities and differences between them, and efficient algorithms will be designed to compute these representations. Based on these summaries, methods will be developed to estimate a trajectory from a given collection, compare trajectories to each other in the context of a collection, and retrieve trajectories from a collection in response to a query. Trajectory collections will also be used to infer information about the environment and the mobile entities involved in these motions.