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

大数据通常来自多个来源，给出的集合包含来自不同观察者的同一对象、空间或现象的多个、往往是部分的“观点”。从这样的数据集中稳健地提取信息需要对大量数据集进行联合分析。该项目正在开发一种新的几何框架，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。虽然这种方法显然适用于具有明确几何特征的数据(例如，图像中的对象)，但该工作也适用于各种数据集，如计算机网络(识别子网络中的共同结构)和海量开放在线课程作业数据(自动携带对其他学生家庭作业中类似问题的评分器注释)。该框架基于考虑对象(点云、图形、图像等)之间的地图构建，以及对地图网络的分析，作为提取信息、为数据生成潜在模型以及传输或推断功能/语义信息的一种方式。这些任务定义了数据集之间地图处理的新领域，并需要具有新思想的工具集，这些工具集来自数学中的泛函分析、非凸优化和同调代数，以及计算机科学中的几何算法、机器学习、优化和逼近算法。还将研究用于解决框架内出现的大规模非线性优化问题的复杂算法技术。

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.