Sheaves：大数据的拓扑方法
Sheaves: A Topological Approach to Big Data
摘要：
本文档开发了用于提取嵌入在具有成对关系（例如因果类型关系）的大型图或数据集中的知识的一般概念。除了数据可以以对象/事件之间的成对关系的形式呈现之外，几乎没有做出任何潜在的假设。这个假设用于挖掘数据集中的模式，定义一个简化的图或数据集，将信息浓缩或集中到一个更紧凑的形式。所得到的提取结构或模式集本质上是明显符号化的，因为它们根据（生成）语法捕获和编码数据集的图结构。这种结构被认为具有层的形式数学结构。本质上，本文将层理论的基本概念引入到图形数据集领域。
英文摘要：
This document develops general concepts useful for extracting knowledge embedded in large graphs or datasets that have pair-wise relationships, such as cause-effect-type relations. Almost no underlying assumptions are made, other than that the data can be presented in terms of pair-wise relationships between objects/events. This assumption is used to mine for patterns in the dataset, defining a reduced graph or dataset that boils-down or concentrates information into a more compact form. The resulting extracted structure or set of patterns are manifestly symbolic in nature, as they capture and encode the graph structure of the dataset in terms of a (generative) grammar. This structure is identified as having the formal mathematical structure of a sheaf. In essence, this paper introduces the basic concepts of sheaf theory into the domain of graphical datasets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
