# Bridging Graph Drawing and Dimensionality Reduction with Stochastic Stress Optimization

arXiv: https://arxiv.org/abs/2605.00641 · HTML: https://mlsanity.com/paper/2605.00641/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 14 references that are in the map.
- First posted on arXiv 1 May 2026.

## Builds on (most cited first, 5 of 5)

- [Stochastic Multidimensional Scaling](https://mlsanity.com/paper/1612.07089/) (2016)
- [When Dimensionality Reduction Meets Graph (Drawing) Theory: Introducing a Common Framework, Challenges and Opportunities](https://mlsanity.com/paper/2412.06555/) (2024)
- [Stochastic Gradient Descent Works Really Well for Stress Minimization](https://mlsanity.com/paper/2008.10376/) (2020)
- [The Perception of Stress in Graph Drawings](https://mlsanity.com/paper/2409.04493/) (2024)
- [FORBID: Fast Overlap Removal By stochastic gradIent Descent for Graph Drawing](https://mlsanity.com/paper/2208.10334/) (2022)

## Abstract (arXiv)

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.