What is the most appropriate way to cluster respondents based on their rankings of some items? I have ~30 observations of individuals ranking 20 different products from top to bottom (1-20). I would like to have a way to "cluster" these individuals based on their rankings of the different products.
For example, I would like to cluster respondents with similar high rankings of the same products. This can be done looking at only the top 3 products ranked by each respondent, if that's simpler.
What would be an appropriate way to perform this analysis?
 A: You can simply use k-means or hierarchical clustering.
However I'd assume the top products are much more carefully ranked and important, so I'd apply the square root to the entire matrix first, or the logarithm. But that is not "guaranteed" to be better.
A: Clustering of respondents based on their rankings of some items - I like to do hierarchical cluster analysis (for example, average or complete linkage) based on Canberra distance or Clark distance. These measures weigh the difference 1-2 higher than 2-3, higher than 3-4, etc. in a exponentially fading manner. It is like podium positions in sports: the advantage of gold (1 place) over silver (2 place) is greater than of silver (2) over bronze (3); while advantage of some 10th place over 11th one is already negligible.
To see the formulas of these two and of many other popular distance measures used for quantitative data - open Word doc. describing my macro !PROXQNT - find it in collection "Various proximities", on my web-page (the link to the page is on my profile page here).
A: Prepare metric to measure distance between rankings (maybe Levenshtein https://en.wikipedia.org/wiki/Levenshtein_distance or Kendall? https://en.wikipedia.org/wiki/Kendall_tau_distance), then use k-centroid.
If you use it for analyzing or visualization the data you can also use HAC.
