Collaborative Research: Joint Analysis of Correlated Data

在科学、工程、医学和商业领域，我们面临着来自传感器、来自模拟或来自互联网上无数个人活动的大量数据。此外，我们收集的数据集经常是高度相互关联的，反映了关于世界上相同或相似/相关实体的信息，或者呼应了人造和自然对象共同的语义上重要的重复/对称或层次结构。该项目将帮助使用相关数据集的科学家和工程师从他们的数据中获得最多的信息和价值。这一方法的关键是联合数据分析的概念，即最好不是孤立地理解每一条数据，而是在相关数据集的同行和合作伙伴提供的背景下，利用上文提到的关系网络。其主要目的是用并行网络来补充科学家和工程师目前存在的社交网络，这些并行网络将他们工作所依据的数据相互链接，使用特定于领域的语义链接，并旨在建立允许在同一领域的科学家使用的数据之间通过算法传输信息的机制。由此产生的系统通过允许一位科学家对一条数据的观察自动传输到其他相关数据集并进行聚合，从而扩大了科学洞察力，还能够自动发现可以向多个数据集提供信息的共享结构或共同抽象。为了完成这种联合分析，该项目将数据集连接到网络中，信息可以沿着这些网络传输和聚合。这些数据集链基于使用特定于领域的特征的高效匹配算法。在相关设置中，这些匹配或地图不是用来估计距离或相似性，而是用来构建可以在不同数据集之间传输信息的运算符。研究团队将利用一个功能分析框架，该框架允许将信息编码为数据上的函数，并产生用于映射的线性运算符，从而能够使用许多来自线性代数和优化的强大工具。利用同调代数的灵感，这个团队将把多个相关的数据集连接到通过这些运算符连接的网络中，以允许信息传输、校正和聚合的方式，最终目标是利用“集合的智慧”为特定的科学家提供尽可能多的特定数据集的信息。

Across science, engineering, medicine and business we face a deluge of data coming from sensors, from simulations, or from the activities of myriads of individuals on the Internet. Furthermore, the data sets we collect are frequently highly inter-correlated, reflecting information about the same or similar/related entities in the world, or echoing semantically important repetitions/symmetries or hierarchical structures common to both man-made and natural objects. This project will assist scientists and engineers working with correlated data sets in getting the most information and value out of their data. Key to the approach is the idea of joint data analysis, the notion that each piece of data is best understood not in isolation but in the context provided by its peers and partners in a collection of related data sets, using the web of relationships referred to above. The key aim is to complement the social networks of scientists and engineers as they exist today with parallel networks that interlink the data they base their work on, using domain-specific semantic links and aiming at mechanisms that allow algorithmic transport of information between data used by scientists working in the same domain. The resulting system amplifies scientific insights by allowing an observation of one scientist on one piece of data to automatically be transported to other relevant data sets and aggregated and also enables the automated discovery of shared structures or common abstractions that can inform multiple data sets.In order to accomplish this joint analysis this project interconnects data sets into networks along which information can be transported and aggregated. These data set links are based on efficient matching algorithms using domain-specific features. In the associated setting, these matching or maps are used not to estimate distances or similarities but to build operators that can transport information between different data sets. The research team will exploit a functional analytic framework that allows for encoding of information as functions over the data and leads to linear operators for mapping, enabling the use of many powerful tools from linear algebra and optimization. Using inspiration from homological algebra, this team will join multiple related data sets into networks connected through these operators in a way that allows information transport, correction, and aggregation, with the ultimate goal of using the "wisdom of the collection" to provide as much information as possible for specific data sets to specific scientists.