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，以及此类数据中依赖关系的估计和表征。 一个目标是开发有效的多尺度算法来近似扫描统计（又名匹配滤波器），以及基于邻近图的扫描统计的替代方法。 这些方法将在表现出时空依赖性的数据的背景下进行分析。 类似的问题，检测的依赖关系，这在图像的背景下，可以适用于检测纹理对象，也将得到解决。在这个数据集规模巨大的时代，相关的兴趣是，当目标是检测给定（或假设）信噪比的信号时，需要观察多少数据的问题。 研究人员还将开发多尺度方法来估计一维和更高维度的长期依赖性。 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吸引人作为测试床。在大量的应用中，时空数据被收集来监控感兴趣的区域。 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检测和防火;或基于医院急诊室访问，救护车调度电话和药房销售的症状监测。 这些被收集的大量数据在正确分析之前是没有用的，它们的分析需要新的方法，既要很好地理解（有数学支持），又要可扩展。 该提案的重点是在监控数据的背景下，无论是从传感器网络或图像，特别是当数据表现出依赖性，这是经常的情况下，新的方法来检测;和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，在检测肿瘤或在功能磁共振成像中可视化大脑活动时的医学成像。 这项研究计划有一个重要的教育组成部分，因为它将涉及至少一名研究生和一名博士后研究人员。

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.