# multidimensional scaling

## Summary

Multidimensional scaling is a method for visualizing similarity between data points by embedding the data into a low-dimensional subspace. The locations are chosen so that the distances in the embedding space match the dissimilarities as closely as possible.

## Context

This concept has the prerequisites:

- optimization problems (Multidimensional scaling is formulated as an optimization problem.)

## Goals

- Know what stress function multidimensional scaling is minimizing

- Understand how it can be used to visualize similarity data

- Be aware that the exact solution can be computed efficiently

## Core resources (we're sorry, we haven't finished tracking down resources for this concept yet)

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ The Elements of Statistical Learning

A graudate-level statistical learning textbook with a focus on frequentist methods.

## -Paid-

→ Multidimensional scaling, tree-fitting, and clustering

## See also

- MDS is closely related to kernel PCA
- MDS can be generalized to metrics other than Euclidean
- Weighted MDS gives a way to uncover meaningful axes by simultaneously modeling multiple similarity matrices
- Other algorithms for learning nonlinear embeddings include:
- Isomap , which tries to model distances along a neighborhood graph
- locally linear embedding
- t-SNE , an embedding which tries to model short distances and ignore long ones
- Gaussian process latent variable models , a Bayesian model similar in spirit to MDS