CIF: Small: Multiresolution Analysis of Graphs

CIF：小：图形的多分辨率分析

• 批准号: 1421919
• 负责人: Jelena Kovacevic
• 金额: $ 15万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-09-01 至 2017-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1421919&HistoricalAwards=false
• 关键词: CIF; Small; Multiresolution; Analysis; Graphs

Datasets that are collected in engineering, social, commercial and other domains are becoming increasingly larger, complex and irregular in structure. There is an urgent need for the development of methods that formalize and automate analysis of such data and are capable of extracting valuable information. Recently, a theoretical framework called signal processing on graphs has emerged as a new approach to analyze data with irregular structure; it extends fundamental signal processing concepts to data residing on arbitrary graphs, as well as formulates data analysis problems as standard signal processing tasks. Moreover, as data often needs to be analyzed at multiple levels of detail, the investigators develop the fundamentals of the multiresolution analysis on graphs, extending the theory of discrete signal processing on graphs.This research extends relevant signal processing concepts that are critical to the development of the multiresolution analysis, including signal translation, scaling, and sampling, to general graphs. The generalized definition is consistent with the classical multiresolution theory for time data and images; it also addresses additional challenges presented by structures and properties of graphs. Additionally, this research involves techniques and devices for the application and implementation of multiresolution analysis methods to data on graphs. The investigators also develop a set of general, theoretical methodologies that can later be instantiated and applied to datasets of different origin, nature and structure.

在工程，社会，商业和其他领域收集的数据集变得越来越大，复杂且不规则。 迫切需要开发对此类数据进行正式和自动化分析的方法，并能够提取有价值的信息。最近，在图上出现了一个称为信号处理的理论框架，已成为一种新方法，用于分析具有不规则结构的数据。它将基本信号处理概念扩展到位于任意图上的数据，并将数据分析问题作为标准信号处理任务。此外，由于数据通常需要在多个详细层面上进行分析，因此研究人员开发了图形上多解析分析的基本原理，从而将离散信号处理的理论扩展到图上。这项研究扩展了相关信号处理概念，这些概念扩展了对多分辨率分析的开发至关重要的，包括信号转换，缩放，缩放，缩放，缩放，缩放和采样图表。广义定义与时间数据和图像的经典多分辨率理论一致。它还解决了图形的结构和属性提出的其他挑战。此外，这项研究涉及用于应用和实施多分辨率分析方法到图上数据的技术和设备。研究人员还开发了一组一般的理论方法论，后来可以实例化并应用于不同来源，性质和结构的数据集。