# Global Minima by Penalized Full-dimensional Scaling

arXiv: https://arxiv.org/abs/2407.16645 · HTML: https://mlsanity.com/paper/2407.16645/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 15 references that are in the map.
- First posted on arXiv 23 Jul 2024.

## Builds on (most cited first, 1 of 1)

- [A Unifying Theory of Exactness of Linear Penalty Functions](https://mlsanity.com/paper/1802.00404/) (2018)

## Abstract (arXiv)

The full-dimensional (metric, Euclidean, least squares) multidimensional scaling stress loss function is combined with a quadratic external penalty function term. The trajectory of minimizers of stress for increasing values of the penalty parameter is then used to find (tentative) global minima for low-dimensional multidimensional scaling. This is illustrated with several one-dimensional and two-dimensional examples.