Application of Mathematical Optimization in Data Visualization and Visual Analytics: A Survey

IF 7.5 3区计算机科学 Q1 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Big Data Pub Date : 2023-03-27 DOI:10.1109/TBDATA.2023.3262151

Guodao Sun;Zihao Zhu;Gefei Zhang;Chaoqing Xu;Yunchao Wang;Sujia Zhu;Baofeng Chang;Ronghua Liang

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引用次数: 2

Abstract

Mathematical optimization is the process of determining the set of globally or locally optimal parameters in a finite or infinite search space. It has been extensively employed in the research areas of computer science, engineering, operations research, and economics. The application of mathematical optimization has also been extended to data visualization, where it can enhance data processing, structure visualization, and facilitate exploration. However, the current state of summarization in the application of mathematical optimization in data visualization remains inadequate. In this article, we review and classify the existing techniques for advanced mathematical optimization in the fields of data visualization and visual analytics. The classification is conducted based on a classical visualization pipeline, including data enhancement and transformation, representation and rendering, as well as interactive exploration and analysis. We also discuss various mathematical optimization models and their solution methods to help readers gain a better understanding of the relationship among models, visualization, and application scenarios. We additionally provide an online exploration demo, which could enable users to interactively find relevant articles. Based on the limitations and potential trends revealed in the existing literature, we define future challenges in the cross-disciplinary of mathematical optimization and data visualization.

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数学优化在数据可视化和可视化分析中的应用综述

数学优化是在有限或无限搜索空间中确定全局或局部最优参数集的过程。它被广泛应用于计算机科学、工程、运筹学和经济学的研究领域。数学优化的应用也扩展到了数据可视化，它可以增强数据处理、结构可视化，并便于探索。然而，目前数学优化在数据可视化中的应用综述仍然不足。在本文中，我们回顾并分类了数据可视化和可视化分析领域中现有的高级数学优化技术。分类是基于经典的可视化管道进行的，包括数据增强和转换、表示和渲染，以及交互式探索和分析。我们还讨论了各种数学优化模型及其解决方法，以帮助读者更好地理解模型、可视化和应用场景之间的关系。我们还提供了一个在线探索演示，使用户可以交互式地查找相关文章。基于现有文献中揭示的局限性和潜在趋势，我们定义了数学优化和数据可视化交叉学科的未来挑战。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IEEE Transactions on Big Data Multiple-

CiteScore

11.80

自引率

2.80%

发文量

114

期刊介绍： The IEEE Transactions on Big Data publishes peer-reviewed articles focusing on big data. These articles present innovative research ideas and application results across disciplines, including novel theories, algorithms, and applications. Research areas cover a wide range, such as big data analytics, visualization, curation, management, semantics, infrastructure, standards, performance analysis, intelligence extraction, scientific discovery, security, privacy, and legal issues specific to big data. The journal also prioritizes applications of big data in fields generating massive datasets.