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. 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.

本研究针对UMAP方法在高维数据降维中的吸引力和排斥力问题进行分析，以揭示其对聚类形成和可视化的影响。论文提出了一种通过调整吸引力以改善聚类一致性的新方法，显著提高了UMAP及类似嵌入方法的可解释性、鲁棒性和准确性。

UMAP中的吸引力形状：探讨降维中的嵌入力