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正变得越来越大，结构越来越复杂和不规则。迫切需要发展一种方法，使这些数据的分析形式化和自动化，并能够提取有价值的信息。最近，一种被称为图上信号处理的理论框架作为一种分析不规则结构数据的新方法出现了；它将基本的信号处理概念扩展到任意图形上的数据，并将数据分析问题表述为标准的信号处理任务。此外，由于数据经常需要在多个细节层面进行分析，研究人员开发了图上的多分辨率分析的基础，扩展了图上的离散信号处理理论。本研究扩展了相关的信号处理概念，这些概念对多分辨率分析的发展至关重要，包括信号转换，缩放和采样，到一般图形。广义定义与时间数据和图像的经典多分辨率理论一致；它还解决了图的结构和属性所带来的额外挑战。此外，本研究还涉及到多分辨率数据分析方法在图形上的应用和实现的技术和设备。研究人员还开发了一套通用的理论方法，这些方法可以稍后实例化并应用于不同来源、性质和结构的数据集。