邻域嵌入中的吸引-排斥谱
Attraction-Repulsion Spectrum in Neighbor Embeddings
AI总结：
本文提出邻域嵌入算法存在吸引-排斥谱：通过调节t-SNE的吸引力与排斥力权衡，可更好地表示连续流形或离散聚类结构。研究证明UMAP、ForceAtlas2和Laplacian Eigenmaps等算法均可归入该谱系，揭示了它们之间固有的权衡关系。
摘要：
邻域嵌入是一类利用 $k$NN 图对复杂高维数据集进行可视化的方法。为了找到低维嵌入，这些算法将相邻点对之间的吸引力与所有点之间的排斥力结合起来。此类算法中最受欢迎的例子之一是 t-SNE。在这里，我们经验性地证明，使用 exaggeration 参数改变 t-SNE 中吸引力与排斥力之间的平衡会产生一个嵌入谱，其特征是一个简单的权衡：更强的吸引力能更好地表示连续的流形结构，而更强的排斥力能更好地表示离散的聚类结构，并产生更高的 $k$NN 召回率。我们发现 UMAP 嵌入对应于增加了吸引力的 t-SNE；数学分析表明，这是因为 UMAP 采用的负采样优化策略强烈降低了有效排斥力。同样地，常用于可视化发育单细胞转录组数据的 ForceAtlas2，产生的嵌入对应于吸引力进一步增加的 t-SNE。位于该谱系极端的是 Laplacian Eigenmaps。我们的结果表明，许多著名的邻域嵌入算法可以被置于吸引-排斥谱上，并突显了它们之间固有的权衡。
英文摘要：
Neighbor embeddings are a family of methods for visualizing complex high-dimensional datasets using $k$NN graphs. To find the low-dimensional embedding, these algorithms combine an attractive force between neighboring pairs of points with a repulsive force between all points. One of the most popular examples of such algorithms is t-SNE. Here we empirically show that changing the balance between the attractive and the repulsive forces in t-SNE using the exaggeration parameter yields a spectrum of embeddings, which is characterized by a simple trade-off: stronger attraction can better represent continuous manifold structures, while stronger repulsion can better represent discrete cluster structures and yields higher $k$NN recall. We find that UMAP embeddings correspond to t-SNE with increased attraction; mathematical analysis shows that this is because the negative sampling optimisation strategy employed by UMAP strongly lowers the effective repulsion. Likewise, ForceAtlas2, commonly used for visualizing developmental single-cell transcriptomic data, yields embeddings corresponding to t-SNE with the attraction increased even more. At the extreme of this spectrum lie Laplacian Eigenmaps. Our results demonstrate that many prominent neighbor embedding algorithms can be placed onto the attraction-repulsion spectrum, and highlight the inherent trade-offs between them.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
