ATD: Detection of Clusters in Spatial Data and Images

研究人员将解决空间/时间数据（如图像或传感器网络）中异常检测的相互关联问题，以及这些数据中依赖性的估计和表征。一个目标是开发有效的多尺度算法来近似扫描统计量（又名匹配滤波器），以及基于接近图的扫描统计量的替代方法。这些方法将在显示时空依赖性的数据上下文中进行分析。检测依赖关系的类似问题，在图像的上下文中可以应用于检测纹理对象，也将被解决。在这个数据集规模巨大的时代，一个相关的问题是，当目标是在给定（或假设）信噪比下检测信号时，需要观察多少数据。研究人员还将开发多尺度方法来估计一维和更高维度的远程依赖关系。在离散数据的情况下，他们将分析伯努利网络中可能的相关结构，这在理论和实践中都是一个有趣的问题，因为它们的简单性使这种网络作为试验台具有吸引力。在大量的应用中，收集时空数据来监视感兴趣的区域。这些方法多种多样，如基于传感器阵列的目标跟踪；基于卫星图像的人造物体探测与防火或者基于医院急诊科就诊、救护车调度电话和药房销售的综合征监测。收集到的大量数据只有经过适当的分析才能发挥作用，而这些数据的分析需要既易于理解（有数学支持）又可扩展的新方法。本提案的重点是在监测数据背景下的新检测方法，无论是来自传感器网络还是图像，特别是当数据表现出依赖性时，这通常是情况；以及依赖性的表征和量化。这项提案中的研究将对整个科学产生影响，例如，在医学成像中检测肿瘤或在fMRI中可视化大脑活动。这个研究计划有一个重要的教育组成部分，它将涉及至少一名研究生和一名博士后研究员。

The investigators will address the inter-related problems of anomaly detection in spatial/temporal data (such as images or sensor networks) and the estimation and characterization of dependencies in such data. One objective is to develop efficient multiscale algorithms for approximating the scan statistic (aka a matched filter), as well as alternative methods to the scan statistic based on proximity graphs. These methods will be analyzed in the context of data that exhibit spatio-temporal dependencies. The analogous problem of detecting dependencies, which in the context of images can be applied to detecting textured objects, will also be tackled. Of related interest in this era of datasets of enormous sizes, is the question of how much of the data is required to be observed when the goal is to detect a signal at a given (or assumed) signal-to-noise ratio. The investigators will also develop multiscale methods for estimating long-range dependencies in one and higher dimensions. In the case of discrete data, they will analyze possible correlation structures in Bernoulli networks, an interesting question both in theory and practice, since their simplicity makes such networks appealing as test beds.In a large number of applications, space-time data are collected to monitor an area of interest. These are as varied as target tracking based on an array of sensors; man-made object detection and fire prevention based on satellite images; or syndromic surveillance based on hospital emergency department visits, ambulance dispatch calls and pharmacy sales. These huge quantities of data being collected are not useful until properly analyzed, and their analysis requires novel methodology that is both well-understood (with mathematical backing) and scalable. The focus of this proposal is on novel approaches to detection in the context of surveillance data, either from sensor networks or images, particularly when the data exhibit dependencies, which is often the case; and on the characterization and quantification of dependencies. The research in this proposal will have an impact on the sciences at large, for example, in medical imaging when detecting tumors or visualizing the brain activity in fMRI. This research plan has an important educational component in that it will involve at least one graduate student and one postdoctoral researcher.