BIGDATA: Collaborative Research: F: From Data Geometries to Information Networks

BIGDATA：协作研究：F：从数据几何到信息网络

基本信息

批准号：
1546392
负责人：
Mauro Maggioni
金额：
$ 50万
依托单位：
Duke University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2016
资助国家：
美国
起止时间：
2016-01-01 至 2017-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1546392&HistoricalAwards=false
关键词：
BIGDATA Collaborative Research Data Geometries

项目摘要

Big Data often results from multiple sources, giving collections that contain multiple, often partial, "views" of the same object, space, or phenomenon from various observers. Extracting information robustly from such data sets calls for a joint analysis of a large collection of data sets. The project is developing a novel geometric framework for modeling, structure detection, and information extraction from a collection of large related data sets, with an emphasis on the relationships between data. While this approach clearly applies to data with a clear geometric character (e.g., objects in images), the work is also applied to datasets as diverse as computer networks (identifying common structure in subnets) and Massive Open Online Course homework data (automatically carrying grader annotations to similar problems in other students' homeworks).The novel framework is based on the construction of maps between the objects under considerations (point clouds, graphs, images, etc...), and on the analysis of the networks of maps that result as a way of extracting information, generating latent models for the data, and transporting or inferring functional / semantic information. These tasks define a new field of map processing between data sets and require tool sets with new ideas from functional analysis, non-convex optimization, and homological algebra in mathematics, and geometric algorithms, machine learning, optimization, and approximation algorithms in computer science. Sophisticated algorithmic techniques for attacking the large-scale non-linear optimization problems that emerge within the framework will also be investigated.

大数据通常来自多个来源，这些来源提供了包含来自各种观察者的同一对象，空间或现象的多个部分的“视图”的集合。从此类数据集中强烈提取信息，要求对大量数据集进行联合分析。该项目正在开发一个新颖的几何框架，用于从大型相关数据集的集合中进行建模，结构检测和信息提取，重点是数据之间的关系。虽然这种方法清楚地适用于具有清晰几何特征（例如，图像中的对象）的数据，但该工作也适用于像计算机网络（确定子网中的常见结构）和大量开放的在线课程家庭作业数据一样多样化的数据集（自动携带渐变器注释（自动携带给其他学生框架）的相似问题。以及对地图网络的分析，这些网络是一种提取信息，为数据生成潜在模型以及运输或推断功能 /语义信息的方式。这些任务在数据集之间定义了一个新的地图处理领域，并需要工具集，其中包括功能分析，非convex优化和数学中的同源代数以及几何算法，计算机科学中的机器学习，优化和近似算法的新想法。还将研究用于攻击框架内出现的大规模非线性优化问题的复杂算法技术。