A first line of attack in exploratory data analysis is data visualization,
i.e., generating a 2-dimensional representation of data that makes clusters of
similar points visually identifiable. Standard Johnson-Lindenstrauss
dimensionality reduction does not produce data visualizations. The t-SNE
heuristic of van der Maaten and Hinton, which is based on non-convex
optimization, has become the de facto standard for visualization in a wide
range of applications.
This work gives a formal framework for the problem of data visualization -
finding a 2-dimensional embedding of clusterable data that correctly separates
individual clusters to make them visually identifiable. We then give a rigorous
analysis of the performance of t-SNE under a natural, deterministic condition
on the "ground-truth" clusters (similar to conditions assumed in earlier
analyses of clustering) in the underlying data. These are the first provable
guarantees on t-SNE for constructing good data visualizations.
We show that our deterministic condition is satisfied by considerably general
probabilistic generative models for clusterable data such as mixtures of
well-separated log-concave distributions. Finally, we give theoretical evidence
that t-SNE provably succeeds in partially recovering cluster structure even
when the above deterministic condition is not met.

通过建立数据可视化形式的二维嵌入来正确地分离数据簇，使用 t-SNE 启发式的数据可视化方法在广泛的应用场景中成为事实上的标准，该研究提供了一种正式框架和分析，以分析数据可视化问题下 t-SNE 的性能表现，并且在满足特定条件时能部分恢复聚类结构。