当降维遇上图（绘制）理论：通用框架、挑战与机遇介绍
When Dimensionality Reduction Meets Graph (Drawing) Theory: Introducing a Common Framework, Challenges and Opportunities
AI总结：
本文提出统一框架弥合降维（DR）与图（绘制）理论的学科鸿沟，借助图论优化DR可视化全流程，拆解DR阶段并适配前沿技术，利用图分析方法改进DR的拓扑提取、嵌入生成与验证，同时指出实施挑战与未来研究方向。
摘要：
在可视化研究的广阔领域中，降维（Dimensionality Reduction, DR）与图分析是两个热门子领域，通常是大多数可视化数据分析配置中的核心环节。DR旨在生成表征，以支持对复杂大型数据集的邻域与相似性分析。图分析则聚焦于识别网络化数据中的显著拓扑属性与关键节点，并有专门研究探索如何向用户呈现此类特征，以降低对底层结构的理解难度。尽管这两个学科通常被视为互不相交的子领域，但我们认为二者存在极强的相似性与协同效应，有望实现双向增益。因此，本文讨论并提出了一个统一框架，以助力弥合DR与图（绘制）理论之间的鸿沟。我们的目标是借助具备扎实数学基础的图论，优化DR可视化表征生成的全流程。我们提出了将DR流程拆解为明确定义阶段的方法，探讨了如何将部分DR前沿技术适配至该框架，并阐述了如何利用图绘制、拓扑特征以及图分析中常用的算法与策略，来改进DR的拓扑提取、嵌入生成与结果验证。我们还讨论了该框架在实施与应用过程中的挑战，明确了相关机遇，为未来的可视化研究指明了方向。
英文摘要：
In the vast landscape of visualization research, Dimensionality Reduction (DR) and graph analysis are two popular subfields, often essential to most visual data analytics setups. DR aims to create representations to support neighborhood and similarity analysis on complex, large datasets. Graph analysis focuses on identifying the salient topological properties and key actors within networked data, with specialized research on investigating how such features could be presented to the user to ease the comprehension of the underlying structure. Although these two disciplines are typically regarded as disjoint subfields, we argue that both fields share strong similarities and synergies that can potentially benefit both. Therefore, this paper discusses and introduces a unifying framework to help bridge the gap between DR and graph (drawing) theory. Our goal is to use the strongly math-grounded graph theory to improve the overall process of creating DR visual representations. We propose how to break the DR process into well-defined stages, discussing how to match some of the DR state-of-the-art techniques to this framework and presenting ideas on how graph drawing, topology features, and some popular algorithms and strategies used in graph analysis can be employed to improve DR topology extraction, embedding generation, and result validation. We also discuss the challenges and identify opportunities for implementing and using our framework, opening directions for future visualization research.
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。
