将降维与图论结合,提升可视化效果的科学性与可解释性。
When Dimensionality Reduction Meets Graph (Drawing) Theory: Introducing a Common Framework, Challenges and Opportunities
- 提出统一框架,分阶段优化降维流程
- 用图论方法改进拓扑保持与嵌入生成
- 适合可视化研究者与数据科学家参考
在可视化研究领域,降维(DR)与图分析是两个重要子方向,常用于复杂数据的可视化分析。降维旨在生成支持邻近关系与相似性分析的低维表示;图分析则关注网络数据中的关键拓扑特征与核心节点,并研究如何向用户呈现这些特征以提升对数据结构的理解。尽管两者常被视为独立领域,本文指出二者存在深层相似性与协同潜力。为此,本文提出一个统一框架,利用坚实的图论基础改进降维可视化全过程。我们把降维过程分解为若干明确阶段,探讨如何将当前主流降维技术映射到该框架中,并提出将图绘制、拓扑特征及常用图分析算法策略应用于降维中的拓扑提取、嵌入生成与结果验证。同时,本文讨论了实施该框架面临的挑战,并指明未来研究方向。
原文摘要 · Abstract (English)
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.
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