# Subspace Least Squares Multidimensional Scaling

arXiv: https://arxiv.org/abs/1709.03484 · HTML: https://mlsanity.com/paper/1709.03484/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Sep 2017.

## Built on by (most cited first, 1 of 1)

- [Unsupervised Manifold Alignment with Joint Multidimensional Scaling](https://mlsanity.com/paper/2207.02968/) (2022)

## Abstract (arXiv)

Multidimensional Scaling (MDS) is one of the most popular methods for dimensionality reduction and visualization of high dimensional data. Apart from these tasks, it also found applications in the field of geometry processing for the analysis and reconstruction of non-rigid shapes. In this regard, MDS can be thought of as a textitshape from metric algorithm, consisting of finding a configuration of points in the Euclidean space that realize, as isometrically as possible, some given distance structure. In the present work we cast the least squares variant of MDS (LS-MDS) in the spectral domain. This uncovers a multiresolution property of distance scaling which speeds up the optimization by a significant amount, while producing comparable, and sometimes even better, embeddings.