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