FastUMAP通过双分图采样加速降维，适合反复探索数据。
FastUMAP: Scalable Dimensionality Reduction via Bipartite Landmark Sampling
- 采用地标点构建稀疏双分图，提升计算效率
- 在MNIST上仅需4.6秒，比t-SNE快约10倍
- 适合快速迭代分析，非追求最高精度场景
高维数据的探索性分析通常需要多次运行降维。实践中，分析师会因预处理、子集或超参数变化而重复执行，传统非线性方法常成为瓶颈。我们提出FastUMAP（双分图流形近似与投影），一种基于地标点的方法，专为重复使用场景设计。FastUMAP构建稀疏点-地标模糊图，从诱导地标相似性中计算Nystrom谱热启动，并在双分图上用UMAP式目标优化所有样本坐标。地标比例r = m/n可直接权衡运行时间与保真度。在9个基准数据集（样本数178至70,000）上，我们的默认实现对比中，有7个数据集运行时间最短。在MNIST和Fashion-MNIST（n=70,000）上，运行时间约4.6秒，相较Barnes-Hut t-SNE的73–75秒显著加快，同时达到91.4%平均kNN准确率，略低于最强基线的94.6%。因此，FastUMAP应被视为重复探索性嵌入的快速选择，而非以精度优先的方法替代。
原文摘要 · Abstract (English)
Exploratory analysis of high-dimensional data rarely stops at a single embedding. In practice, analysts rerun dimensionality reduction after changing preprocessing, subsets, or hyperparameters, and standard nonlinear methods can quickly become the bottleneck. We introduce FastUMAP (Bipartite Manifold Approximation and Projection), a landmark-based method designed for this repeated-use setting. FastUMAP builds a sparse point-landmark fuzzy graph, computes a Nystrom spectral warm start from the induced landmark affinity, and then refines all sample coordinates with a UMAP-style objective on the bipartite graph. The landmark ratio r = m/n provides a direct way to trade runtime against fidelity. On 9 benchmark datasets spanning 178 to 70,000 samples, FastUMAP has the lowest runtime on 7 datasets in our reported default-implementation comparison on one workstation. On MNIST and Fashion-MNIST (n=70000), it runs in about 4.6 seconds, compared with about 73--75 seconds for Barnes--Hut t-SNE, while reaching 91.4% mean kNN accuracy versus 94.6% for the strongest accuracy baseline. FastUMAP is therefore best viewed as a fast option for repeated exploratory embedding, rather than as a replacement for accuracy-first methods.
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