Understanding How Dimension Reduction Tools Work
Cynthia D Rudin · Proceedings of the International Conference on Statistics, Theory and Applications (ICSTA ...) · 2023
Dimension reduction (DR) techniques such as t-SNE, UMAP, and TriMap have demonstrated impressive visualization performance on many real world datasets. They are useful for understanding data and trustworthy decision-making, particularly for biological data. One tension that has always faced these methods is the apparent trade-off between preservation of global structure and preservation of local structure: past methods can either handle one or the other, but not both. In this work, our goal is to understand what aspects of DR methods are important for preserving both local and global structure. We leverage our insights to design a new algorithm for DR, called Pairwise Controlled Manifold Approximation Projection (PaCMAP), which preserves both local and global structure. Our work provides several unexpected insights into what design choices to make when constructing DR algorithms.