The Shape of Attraction in UMAP: Exploring the Embedding Forces in Dimensionality Reduction
This work enhances interpretability and robustness for users of UMAP and similar dimensionality reduction methods, though it is incremental as it builds on existing techniques.
The paper analyzes the attractive and repulsive forces in UMAP to understand their effects on cluster formation and visualization, leading to modifications that improve consistency under random initialization.
Uniform manifold approximation and projection (UMAP) is among the most popular neighbor embedding methods. The method relies on attractive and repulsive forces among high-dimensional data points to obtain a low-dimensional embedding. In this paper, we analyze the forces to reveal their effects on cluster formations and visualization and compare UMAP to its contemporaries. Repulsion emphasizes differences, controlling cluster boundaries and inter-cluster distance. Attraction is more subtle, as attractive tension between points can manifest simultaneously as attraction and repulsion in the lower-dimensional mapping. This explains the need for learning rate annealing and motivates the different treatments between attractive and repulsive terms. Moreover, by modifying attraction, we improve the consistency of cluster formation under random initialization. Overall, our analysis makes UMAP and similar embedding methods more interpretable, more robust, and more accurate.