#smacof

This is kind of a fun example, and you might find the fuzzy clustering technique useful, as I have, for exploratory data analysis. In this Gist, I use the unparalleled breakfast dataset from the smacof package, derive dissimilarities from breakfast item preference correlations, and use those dissimilarities to cluster foods.

Fuzzy clustering with fanny() is different from k-means and hierarchical clustering, in that it returns probabilities of membership for each observation in each cluster. Here, I ask for three clusters, so I can represent probabilities in RGB color space, and plot text in boxes with the help of this StackOverflow answer.

The colors and the MDS configuration highlight the three primary clusterings of breakfast items into what we'll call a muffin group, a bread group, and a sweet group. Of course, cluster identification is a subjective exercise, made even more so by use of probabilistic membership, but I'm pretty happy with this breakfast analysis.

SMACOF stands for "Scaling by MAjorizing a COmplicated Function," and it is a multidimensional scaling algorithm for metric unfolding of, among other things, rectangular ratings matrices.

One neat Political Science application of MDS is inferring ideology from survey thermometer ratings. The 2008 ANES featured 43 different thermometer stimuli, and today's Gist shows how to use SMACOF to simultaneously scale survey respondents and thermometer stimuli in the same space, and to compare this measure of inferred ideology across partisans.

I've also got a little piece of code that replaces numeric axis labels with names of the stimuli, which I think might be better, as the numbers don't really mean much except in comparison with the stimuli. Let me know what you think!