I'm doing a research project on evaluating Communist party support in the context of the application of Socialism with Chinese Characteristics, relating widespread support for policies with the relevant socialist theory. Anyway, while doing research I stumbled across this usage of K-means clustering to analyze the data and with this application of a data analysis tool, the support for the party, while still high, varies greatly from what is initially suggested from the surveys.
Looking at it I find some of the justifications they use for describing typologies a little fishy. The questions asked are whether or not you trust the CPC on a four point scale with 1 being not at all and 4 being high amounts of trust, with the second question being about support for the one party system using the same scale. In any case they use K Clustering to break these groups into the four possible typologies and cluster the two of the middle groups together under the justification that people can be "ambivalent". However, this feels like unnecessary simplification of the clusters in order to present the "ambivalence" as being more varied than it is. Just because people might have incoherent views on the issue doesn't mean they do and presenting the issue as that feels like it could be "gerrymandering" data. I'm completely open to my speculations and reservations being completely off base, this is very estranged from my major, but I thought I would ask her for some help in understanding it.
You guys are pretty smart sometimes 
The part I'm discussing occurs on page 56 where they begin to explain their statistics and methods.
so they've defined ambivalent typologies based on their framework in table 1, and use that to impose 4 clusters onto the data
so there's really only 3 clusters but they've decided to set k=4 anyway, and then k-means just minimizes the variance within each cluster relative to its mean value. each observation gets assigned to whichever mean is "closest" in a certain sense, but that doesn't mean it's really the best choice.
even after they "merge" the ambivalent classes and set k=3, assigning each observation to a cluster based on the closest mean value doesn't mean it's the best choice for defining each class, just that it's the closest in terms of variance.
the natopedia article has a good illustration:
https://en.wikipedia.org/wiki/K-means_clustering#/media/File:K-means_convergence.gif
Doesn't it seem strange to apply this kind of statistical analysis to a four point survey?
yeah, the more i think about it the more strange it seems. they've already defined groups, just cluster them based on what their answers were. doing an iterative means clustering algorithm seems like they felt like they needed to do some fancy math to make it look better.