CIF: Small: Multiresolution Analysis of Graphs

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、复杂和结构不规则。 目前迫切需要制定方法，使这些数据的分析正规化和自动化，并能够提取有价值的信息。最近，一种称为图上信号处理的理论框架已经成为分析具有不规则结构的数据的新方法;它将基本信号处理概念扩展到驻留在任意图上的数据，并将数据分析问题制定为标准信号处理任务。此外，由于数据往往需要在多个层次的细节进行分析，研究人员开发的多分辨率分析的基本原理图，扩展的离散信号处理理论的graphs.This研究扩展相关的信号处理的概念，是至关重要的多分辨率分析的发展，包括信号的转换，缩放和采样，一般的图形。广义定义与经典的时间数据和图像的多分辨率理论是一致的，它还解决了图的结构和性质所带来的额外挑战。此外，本研究涉及的技术和设备的应用和实施的多分辨率分析方法的数据图。研究人员还开发了一套通用的理论方法，这些方法可以在以后实例化并应用于不同来源，性质和结构的数据集。

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.