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III: Small: Spectral clustering with tensors

III：小：张量谱聚类

基本信息

批准号：
1422918
负责人：
David Gleich
金额：
$ 33.95万
依托单位：
Purdue University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2014
资助国家：
美国
起止时间：
2014-09-01 至 2019-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1422918&HistoricalAwards=false
关键词：
III Small Spectral clustering tensors

项目摘要

Society is awash in complex data that is recorded by high-resolution sensors and through our traces of online activity. One of the key challenges in turning this data into actionable insight is finding hidden groups in these data. For instance, finding similar types of land based on its spectral composition, or finding groups of like-minded people in a social network. While there are a variety of methods to solve these problems that are known already, there are none that take advantage of the multi-dimensional features of the data in an integrated way. The work in this proposal will provide an entirely new type of data clustering, or grouping. The method exploits the rich features of these complex modern datasets. Having access to such a method will help society improve its understanding of the results of complex scientific experiments, produce new insights into the common patterns in social networks, and extract valuable information from large databases of sensor information. The methods developed will be general, and thus, they will have broad applicability that will enrich our capability to use data to benefit society.Spectral clustering is a technique to identify cohesive groups in a database based on simple pairwise relationships between the items. In a social network, for example, people are connected based on pair-wise friendship relationships. This two-way, or two-dimensional, association between people does not capture the richness of real-world social interactions that often involve multiple people. These higher-order interactions among groups will be represented as tensors and hyper-graphs in this project. For instance, an interaction among three people corresponds to a hyper-edge, which will be represented by a three-dimensional tensor. Thus, this project will investigate novel formulations of the spectral clustering problem that work on multi-dimensional relationships represented with tensors. These new methods and their variations will be evaluated based on the insights that they provide into (i) hyper-spectral imaging data, where each pixel has a large number of frequencies measured; (ii) in social network data, where groups of interactions create higher-order relationships; and (iii) in complex simulation data, where parametric variation creates multi-dimensional data and relationships based on space, time and parameters. This project will also investigate fast algorithms to identify the clusters based on the new formulations of spectral clustering, as well as relations between these algorithms and emerging work in computational topology.All of the software developed as part of this project will be released as open source software in order to maximize its impact. The investigator will organize tutorials on these new formulations at major conferences to attract additional applications.For further information see the project web site at: https://www.cs.purdue.edu/homes/dgleich/tensors

社会充斥着复杂的数据，这些数据由高分辨率传感器记录下来，并通过我们的在线活动痕迹记录下来。将这些数据转化为可操作的见解的关键挑战之一是找到这些数据中隐藏的群体。例如，根据光谱组成找到相似类型的土地，或者在社交网络中找到志同道合的人。虽然有各种已知的方法来解决这些问题，但没有一种方法能够以综合的方式利用数据的多维特征。本提案中的工作将提供一种全新类型的数据聚类或分组。该方法利用了这些复杂的现代数据集的丰富特征。获得这种方法将有助于社会提高对复杂科学实验结果的理解，对社会网络中的常见模式产生新的见解，并从大型传感器信息数据库中提取有价值的信息。所开发的方法将是通用的，因此，它们将具有广泛的适用性，这将丰富我们使用数据造福社会的能力。谱聚类是一种基于项之间的简单成对关系来识别数据库中内聚组的技术。例如，在社交网络中，人们是基于成对的友谊关系联系在一起的。人与人之间的这种双向或二维的联系并没有捕捉到现实世界中经常涉及多人的社会互动的丰富性。在这个项目中，这些组之间的高阶相互作用将被表示为张量和超图。例如，三个人之间的互动对应一个超边缘，它将由三维张量表示。因此，本项目将研究用张量表示的多维关系的谱聚类问题的新公式。这些新方法及其变化将根据它们提供的见解进行评估：(1)高光谱成像数据，其中每个像素都有大量测量的频率；（ii）在社交网络数据中，群体互动创造了高阶关系；（iii）在复杂的仿真数据中，参数变化会产生基于空间、时间和参数的多维数据和关系。该项目还将研究基于谱聚类新公式识别聚类的快速算法，以及这些算法与计算拓扑中新兴工作之间的关系。作为该项目的一部分开发的所有软件都将作为开源软件发布，以最大限度地发挥其影响。研究者将在主要会议上组织关于这些新配方的教程，以吸引更多的应用。欲了解更多信息，请参阅该项目的网站：https://www.cs.purdue.edu/homes/dgleich/tensors