对比多种降维方法，发现监督版UMAP在分类中表现好，回归中效果有限。
A Comparative Study of UMAP and Other Dimensionality Reduction Methods
- 用模拟和真实数据系统比较了UMAP及其监督版本与其他降维方法
- 监督版UMAP在分类任务中预测准确率高，回归任务中响应信息利用不足
- 适合关注降维方法性能差异的研究者，尤其关注监督学习场景
均匀流形近似与投影（UMAP）是一种广泛使用的流形学习降维技术。本文对UMAP、监督版UMAP及多种竞争性降维方法（包括主成分分析（PCA）、核PCA、切片逆回归（SIR）、核SIR和t分布随机邻域嵌入）进行了全面比较分析。尽管UMAP在保持局部与全局结构方面备受关注，其监督扩展（尤其在回归场景）仍研究不足。本文通过模拟和真实数据集，系统评估了监督版UMAP在分类与回归中的表现，以低维嵌入的预测准确性为评价标准。结果表明，监督版UMAP在分类任务中表现良好，但在回归任务中未能有效融合响应变量信息，凸显了未来研究的重要方向。
原文摘要 · Abstract (English)
Uniform Manifold Approximation and Projection (UMAP) is a widely used manifold learning technique for dimensionality reduction. This paper studies UMAP, supervised UMAP, and several competing dimensionality reduction methods, including Principal Component Analysis (PCA), Kernel PCA, Sliced Inverse Regression (SIR), Kernel SIR, and t-distributed Stochastic Neighbor Embedding, through a comprehensive comparative analysis. Although UMAP has attracted substantial attention for preserving local and global structures, its supervised extensions, particularly for regression settings, remain rather underexplored. We provide a systematic evaluation of supervised UMAP for both regression and classification using simulated and real datasets, with performance assessed via predictive accuracy on low-dimensional embeddings. Our results show that supervised UMAP performs well for classification but exhibits limitations in effectively incorporating response information for regression, highlighting an important direction for future development.
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