The Shape of Data: A New Way to Detect Critical Shifts in System Performance

数据的形状：检测系统性能关键变化的新方法

• 批准号: 1537460
• 负责人: Elizabeth Bradley
• 金额: $ 43万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-01 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1537460&HistoricalAwards=false
• 关键词: Shape; Data; New; Way; Detect

This project is about a new way to detect and classify shifts in the patterns of measurements taken by sensors. Subtle shifts in the output from a vibration sensor on a bridge abutment, for instance, can indicate that a crack is developing in that structure. Identifying these shifts can be a real challenge because modern sensors can generate so much information, and so quickly. Existing approaches to this use the mathematics of statistics: averages, variability, and the like. This project uses techniques from topology, the branch of mathematics that is concerned with shape, to detect these kinds of shifts.This project will develop techniques to assess and characterize temporal patterns in nonstationary time-series data. The project will compute aspects of the homology---e.g., the first few Betti numbers---of the stream "on the fly" to obtain a signature of its regime. To mitigate the computational burden of traditional techniques, this project uses a simplicial complex based on a small, representative set of "landmarks," with the remaining data, the "witnesses," defining the connections. New techniques include a generalization of the oft-used false near-neighbor method to evaluate the fidelity of the topology of the reconstruction, efficient selection of landmarks and choice of witness relation, classification of structure through multi-parameter persistent homology of embedded data, and development of a map on the witness complex to obtain a dynamical signature of each regime. The goals include efficient detection of regime shifts, the development of a catalog of signatures within regimes, and the detection and mitigation of noise. The classification techniques will be applicable, for example, to the detection of failure modes in manufacturing systems, malware attacks on a network, incipient heart problems, or an impending containment failure.

这个项目是关于一种新的方法来检测和分类传感器测量模式的变化。例如，桥梁桥台上的振动传感器输出的细微变化可能表明该结构中正在出现裂缝。识别这些变化可能是一个真正的挑战，因为现代传感器可以产生如此多的信息，而且如此之快。现有的方法使用统计学的数学方法：平均值、变异性等。这个项目使用拓扑学中与形状有关的数学分支中的技术来检测这些类型的移位。这个项目将开发评估和表征非平稳时间序列数据中的时间模式的技术。该项目将计算溪流的同调的各个方面-例如，前几个Betti数-以获得其制度的签名。为了减轻传统技术的计算负担，该项目使用了一个基于一小部分具有代表性的“地标”的简单复合体，其余数据--“证人”--定义了联系。新技术包括对常用的虚假近邻方法的推广，以评估重建拓扑的保真度，有效地选择地标和选择证人关系，通过嵌入数据的多参数持久同调对结构进行分类，以及在证人复合体上开发地图以获得每个制度的动态签名。这些目标包括有效地检测政权更迭，制定政权内的签名目录，以及检测和减轻噪音。例如，分类技术将适用于检测制造系统中的故障模式、网络上的恶意软件攻击、早期心脏问题或即将发生的遏制故障。

项目成果

Computational Topology Techniques for Characterizing Time-Series Data

用于表征时间序列数据的计算拓扑技术

• DOI: 10.1007/978-3-319-68765-0_24
• 发表时间: 2017
• 期刊: Advances in Intelligent Data Analysis XVI. IDA 2017
• 作者: Sanderson, N.;Shugerman, E;Molna, r S.;Meiss, J.D.;Bradley, E.
• 通讯作者: Bradley, E.