SIAM Review, Volume 64, Issue 1, Page 151-151, February 2022.
The SIAM Journal on Mathematics of Data Science (SIMODS) launched in February 2019. The SIGEST article in this issue, “Dimensionality Reduction via Dynamical Systems: The Case of t-SNE,” by George C. Linderman and Stefan Steinerberger, is therefore our first SIMODS representative. Here the authors study t-SNE, a widely adopted clustering and visualization algorithm proposed by Laurens van der Maaten and Geoffrey Hinton in 2008---that publication has received over 24,000 Google Scholar citations to date. The SIMODS editorial board commented that ``[f]or anyone who tries to interact with people in bioinformatics, they will know that t-SNE is truly one of the most commonly used visualization algorithms, and in those visualizations the interpretation is always about the clusters that arise. Basically, t-SNE was something that was one principled way for dimensionality reduction that got co-opted for so much more. It's a rare theorist that takes what's actually already being used and working, and tries to explain it. This paper is certain to make a long term impact." In this work the authors use a dynamical systems perspective to explain why, and at what rate, the algorithm is guaranteed to converge successfully when applied to data that contains well-separated clusters. They also discuss fundamental connections to spectral clustering algorithms. Throughout, ideas are illustrated via colorful visualizations on both synthetic and real datasets. In preparing the article for SIGEST, the authors have appended the new section 7, which gives a big-picture, accessible overview of the topic. This new section also outlines recent developments in the area and lists a number of open problems.

中文翻译：

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SIGEST

SIAM 评论，第 64 卷，第 1 期，第 151-151 页，2022 年 2 月。
SIAM 数据科学数学杂志 (SIMODS) 于 2019 年 2 月推出。因此，George C. Linderman 和 Stefan Steinerberger 在本期的 SIGEST 文章“通过动态系统进行降维：t-SNE 的案例”是我们的第一位 SIMODS 代表。在这里，作者研究了 t-SNE，这是一种广泛采用的聚类和可视化算法，由 Laurens van der Maaten 和 Geoffrey Hinton 在 2008 年提出——迄今为止，该出版物已收到超过 24,000 次 Google Scholar 引用。SIMODS 编辑委员会评论说``[f] 或任何试图与生物信息学领域的人互动的人，他们都会知道 t-SNE 确实是最常用的可视化算法之一，而在这些可视化中，解释总是关于出现的集群。基本上，t-SNE 是一种用于降维的原则性方法，并被更多地采用。这是一位罕见的理论家，他将实际已经在使用和工作的东西，并试图解释它。这篇论文肯定会产生长期影响。”在这项工作中，作者使用动态系统的视角来解释为什么当应用于包含良好分离的集群的数据时，该算法能够保证成功收敛以及以何种速率收敛。他们还讨论了与光谱聚类算法的基本联系。自始至终，想法都是通过对合成数据集和真实数据集的彩色可视化来说明的。在为 SIGEST 准备文章时，作者附加了新的第 7 节，该节给出了一个宏观的、易于理解的概述话题。