# Multidimensional Scaling, Sammon Mapping, and Isomap: Tutorial and Survey

arXiv: https://arxiv.org/abs/2009.08136 · HTML: https://mlsanity.com/paper/2009.08136/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2020.

## Built on by (most cited first, 13 of 13)

- [Reproducing Kernel Hilbert Space, Mercer's Theorem, Eigenfunctions, Nystr"om Method, and Use of Kernels in Machine Learning: Tutorial and Survey](https://mlsanity.com/paper/2106.08443/) (2021)
- [Fermat Distances: Metric Approximation, Spectral Convergence, and Clustering Algorithms](https://mlsanity.com/paper/2307.05750/) (2023)
- [Spectral, Probabilistic, and Deep Metric Learning: Tutorial and Survey](https://mlsanity.com/paper/2201.09267/) (2022)
- [Efficient channel charting via phase-insensitive distance computation](https://mlsanity.com/paper/2104.13184/) (2021)
- [Laplacian-Based Dimensionality Reduction Including Spectral Clustering, Laplacian Eigenmap, Locality Preserving Projection, Graph Embedding, and Diffusion Map: Tutorial and Survey](https://mlsanity.com/paper/2106.02154/) (2021)
- [Hypothesis-Driven Feature Manifold Analysis in LLMs via Supervised Multi-Dimensional Scaling](https://mlsanity.com/paper/2510.01025/) (2025)
- [Sample-Efficient Geometry Reconstruction from Euclidean Distances using Non-Convex Optimization](https://mlsanity.com/paper/2410.16982/) (2024)
- [Towards a framework on tabular synthetic data generation: a minimalist approach: theory, use cases, and limitations](https://mlsanity.com/paper/2411.10982/) (2024)
- [Collective variable discovery in the age of machine learning: reality, hype and everything in between](https://mlsanity.com/paper/2112.03202/) (2021)
- [Unified Framework for Spectral Dimensionality Reduction, Maximum Variance Unfolding, and Kernel Learning By Semidefinite Programming: Tutorial and Survey](https://mlsanity.com/paper/2106.15379/) (2021)
- [Clustering acoustic emission data streams with sequentially appearing clusters using mixture models](https://mlsanity.com/paper/2108.11211/) (2021)
- [Enhancing Dimension-Reduced Scatter Plots with Class and Feature Centroids](https://mlsanity.com/paper/2403.20246/) (2024)
- [Deep-MDS Framework for Recovering the 3D Shape of 2D Landmarks from a Single Image](https://mlsanity.com/paper/2210.15200/) (2022)

## Abstract (arXiv)

Multidimensional Scaling (MDS) is one of the first fundamental manifold learning methods. It can be categorized into several methods, i.e., classical MDS, kernel classical MDS, metric MDS, and non-metric MDS. Sammon mapping and Isomap can be considered as special cases of metric MDS and kernel classical MDS, respectively. In this tutorial and survey paper, we review the theory of MDS, Sammon mapping, and Isomap in detail. We explain all the mentioned categories of MDS. Then, Sammon mapping, Isomap, and kernel Isomap are explained. Out-of-sample embedding for MDS and Isomap using eigenfunctions and kernel mapping are introduced. Then, Nystrom approximation and its use in landmark MDS and landmark Isomap are introduced for big data embedding. We also provide some simulations for illustrating the embedding by these methods.