# Stochastic Multidimensional Scaling

arXiv: https://arxiv.org/abs/1612.07089 · HTML: https://mlsanity.com/paper/1612.07089/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2016.

## Built on by (most cited first, 6 of 6)

- [A Unified Framework for Optimization-Based Graph Coarsening](https://mlsanity.com/paper/2210.00437/) (2022)
- [Towards Digital Twin Oriented Modelling of Complex Networked Systems and Their Dynamics: A Comprehensive Survey](https://mlsanity.com/paper/2202.09363/) (2022)
- [Unsupervised Manifold Alignment with Joint Multidimensional Scaling](https://mlsanity.com/paper/2207.02968/) (2022)
- [Mapping Research Trajectories](https://mlsanity.com/paper/2204.11859/) (2022)
- [Modularity aided consistent attributed graph clustering via coarsening](https://mlsanity.com/paper/2407.07128/) (2024)
- [Bridging Graph Drawing and Dimensionality Reduction with Stochastic Stress Optimization](https://mlsanity.com/paper/2605.00641/) (2026)

## Abstract (arXiv)

Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates the use of batch optimization algorithms that are not scalable to large-sized problems. This paper considers an alternative stochastic stress minimization framework that is amenable to incremental and distributed solutions. A novel linear-complexity stochastic optimization algorithm is proposed that is provably convergent and simple to implement. The applicability of the proposed algorithm to localization and visualization tasks is also expounded. Extensive tests on synthetic and real datasets demonstrate the efficacy of the proposed algorithm.