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、模拟或互联网上无数个人活动的大量数据。此外，我们收集的数据集通常是高度相互关联的，反映了世界上相同或相似/相关实体的信息，或者反映了人造和自然物体共同的语义重要重复/对称或层次结构。该项目将帮助科学家和工程师使用相关数据集，从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想法，即最好不是孤立地理解每一段数据，而是在同行和伙伴利用上文提到的关系网提供的相关数据集的背景下理解每一段数据。其主要目的是补充科学家和工程师的社交网络，因为他们今天存在的并行网络，互连他们的工作基础上的数据，使用特定领域的语义链接，并旨在机制，允许在同一领域的科学家使用的数据之间的算法传输信息。由此产生的系统通过允许一个科学家对一个数据的观察自动传输到其他相关的数据集和聚合，并使共享结构或共同的抽象，可以通知多个数据集的自动发现放大了科学见解。为了完成这种联合分析，该项目互连数据集到网络沿着的信息可以传输和聚合。这些数据集链接基于使用特定领域特征的高效匹配算法。在相关的设置中，这些匹配或映射不用于估计距离或相似性，而是用于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函数分析框架，该框架允许将信息编码为数据上的函数，并导致线性算子用于映射，从而能够使用线性代数和优化中的许多强大工具。利用同源代数的灵感，该团队将通过这些运算符将多个相关数据集加入到连接的网络中，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.