用随机梯度优化统一降维与图绘制，提速显著且效果不差。
Bridging Graph Drawing and Dimensionality Reduction with Stochastic Stress Optimization
- 用局部成对更新的随机梯度法优化全局应力
- 在标准高维数据集上收敛速度远超SMACOF算法
- 兼容scikit-learn，适合需要高效可视化的研究者
降维（DR）与图绘制（GD）均旨在可视化非线性抽象结构，但采用不同优化范式。尽管多维缩放（MDS）通常依赖SMACOF算法，但图绘制研究显示，针对相同目标，更简单的随机优化方法可能更有效。本文通过将图绘制中的随机梯度下降（SGD）技术引入向量数据嵌入，弥合了这两个领域。我们提出一个兼容scikit-learn的估计器，通过局部成对更新最小化全局应力，改进了现有实现。在标准高维基准测试上，我们的随机求解器收敛速度显著快于SMACOF，同时达到相当或更低的应力值。
原文摘要 · Abstract (English)
Both Dimensionality Reduction (DR) and Graph Drawing (GD) aim to visualize abstract, non-linear structures, yet rely on different optimization paradigms. This contrast is evident in Multidimensional Scaling (MDS), which typically depends on the SMACOF algorithm despite graph drawing results showing that simpler stochastic optimization schemes can be more effective for the same objective. We bridge these domains by adapting Stochastic Gradient Descent (SGD) techniques from graph drawing to vector data embedding. We present a scikit-learn compatible estimator that minimizes global stress through local pairwise updates, improving upon the existing implementation. Experiments on standard high-dimensional benchmarks show that our stochastic solver converges substantially faster than SMACOF while achieving comparable or lower stress.
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