ATD: Detection of Clusters in Spatial Data and Images

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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.