ATD: Detection of Clusters in Distributed Systems of Information under Dependence

ATD：依赖下的分布式信息系统中的集群检测

• 批准号: 1120888
• 负责人: Ery Arias-Castro
• 金额: $ 9.99万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-03-01 至 2014-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1120888&HistoricalAwards=false
• 关键词: ATD; Detection; Clusters; Distributed; Systems

The first part of the proposal deals with detecting correlations. A special case is the problem of testing whether the covariance matrix of a multivariate population is the identity matrix. The investigators will reconsider this classical problem assuming that, under the alternative, only a small fraction of the variables are correlated. The second part of the proposal is focused on determining which correlation structures are possible for Bernoulli random variables. The investigators propose to investigate such algebraic constraints on correlations between Bernoulli random variables under constraints on the correlation structure implied by homogeneity (stationarity) and isotropy, in the case of long range dependence. The third part is on applying resampling techniques to change point analysis of time series and random fields. This is particularly important in detection situations where the underlying distribution of the data is unknown. A recently introduced novel way to bootstrap time series, namely the linear process bootstrap, holds some promise and seems extendable to random fields.The task of anomaly detection is quintessential in surveillance settings where the first step is to detect the presence of an anomaly. Applications range from detecting vehicles that transport hazardous radioactive or bioactive materials, target tracking, man-made object recognition from satellite images, and more. Beyond surveillance, similar detection problems arise in many other areas, such as the detection of fires for satellites, flu outbreaks in an urban area, or the detection of tumors in medical imaging. The investigators will focus on detecting unusual dependencies in the data, on modeling such dependencies and on engineering new ways of calibrating detectors based on carefully designed simulations.

该提案的第一部分涉及检测相关性。一个特殊情况是测试多元总体的协方差矩阵是否为单位矩阵的问题。研究人员将重新考虑这个经典问题，假设在另一种选择下，只有一小部分变量是相关的。该提案的第二部分重点是确定哪些相关结构对于伯努利随机变量是可能的。研究人员建议在长程依赖的情况下，在同质性（平稳性）和各向同性所暗示的相关结构的约束下，研究伯努利随机变量之间相关性的代数约束。第三部分是应用重采样技术对时间序列和随机场进行变点分析。这在数据的底层分布未知的检测情况下尤其重要。最近推出的一种引导时间序列的新颖方法，即线性过程引导，具有一定的前景，并且似乎可以扩展到随机领域。异常检测的任务在监控环境中至关重要，其中第一步是检测异常的存在。应用范围包括检测运输危险放射性或生物活性材料的车辆、目标跟踪、卫星图像中的人造物体识别等等。除了监视之外，类似的检测问题还出现在许多其他领域，例如卫星火灾检测、城市地区流感爆发或医学成像中肿瘤检测。研究人员将专注于检测数据中不寻常的依赖性、对此类依赖性进行建模以及基于精心设计的模拟设计校准探测器的新方法。