scikit-learn/scikit-learn — pull request #797 by NelleV (2012-04-25 22:29:24+00:00)
Title: WIP - adds a MDS algorithm: SMACOF

This is an early PR for MDS (http://en.wikipedia.org/wiki/Multidimensional_scaling)

Multidimensional scaling is a set of statistical algorithms used in information visualization for exploring similarities or dissimilarities in data. Given a similarity or dissimilarity matrix, MDS finds a representation in a small geometric space.

The algorithm implemented here is the SMACOF, which works both for metric and nonmetric MDS. MDS minimises a objective function called stress; the SMACOF algorithm uses the Guttman transform for the metric step (http://en.wikipedia.org/wiki/Stress_majorization, http://cran.r-project.org/web/packages/smacof/vignettes/smacof.pdf)
The nonmetric step is here implemented using the PAVA (Pool Adjancent Violator Algorithm) for the isotonic regression.

Thanks,
N