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Lots of people use cluster analysis. I've heard very few explicitly say why. I imagine this is because within a given field, most researchers seem to understand why clustering is used for the problems typical to that area - but uses vary between fields, and I haven't seen those differences addressed anywhere.

I am particularly interested in the contrast between latent-variable interpretations of model-based methods (mixture models), and clustering applications in machine learning that don't seem as worried about interpretation of clusters, just that they are useful in some way. Data reduction is an even more agnostic application that is very common.

There are loads of papers comparing different methods for clustering - but I can't find any that compare philisophical/theoretical approaches. If you know of any, could you please list them here?

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    $\begingroup$ BTW, Wittgenstein's family resemblance is where early clustering (such as hierarchical methods) stems from. $\endgroup$
    – ttnphns
    Dec 21, 2013 at 9:58
  • $\begingroup$ Define "philosophical." It sounds like a survey on different applications of clustering methods might satisfy you, but I'm not sure that's actually what you want. $\endgroup$
    – David Marx
    Dec 21, 2013 at 10:02
  • $\begingroup$ Yeah, philosophical is a little vague, but for example, some people coming from a latent variable perspective would argue that the clustering has no value if it doesn't reflect something "real" - whereas other people are simply content that a cluster is a useful contruct. $\endgroup$
    – D L Dahly
    Dec 21, 2013 at 10:05
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    $\begingroup$ reflect something "real" - whereas other people content that... is a useful contruct People say the same things about any other type of analysis, not just clustering. This way you will find yourself at the very basic roots of major philosophical distinctions. However, one thing is true about clustering is that it is among the most As you sow so shall you reap techniques: in the sense that any clustering method is full of its own assumptions and is biased to give its "favourite" sort of clusters. $\endgroup$
    – ttnphns
    Dec 21, 2013 at 10:22
  • $\begingroup$ @ttphns The comment on Wittgenstein (W) is puzzling. Generally, principles and practice of classification long predate W. Aristotle discussed classification; hierarchical schemes in biology and elsewhere long predate Linnaeus. Specifically, W's comments on classification are if anything subversive of formal attempts at identifying distinct clusters, not supportive in any sense. $\endgroup$
    – Nick Cox
    Dec 22, 2013 at 19:54

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I like the article entitled Observations on the Use of Growth Mixture Models in Psychological Research. Perhaps not as theoretical as you would like but it is very enlightening. It is written in the context of longitudinal research I think, and within the psychological realm, but a lot can be learned from it.

Edit: Actually, upon second reading there is quite a bit of theoretical/philosophical discussion in that paper! Seems relevant.

Edit: I would also like to add another paper to this answer, entitled What's a taxon? Meehl argues that there are true clusters in nature and provides a salient example there there are gophers, and there are chipmunks, but there are no gophmunks. This does a good job at defining a taxonic group, and highlights that such taxons may also be common in humans. A great deal of research has sought to answer such questions using latent cluster analyses and such.

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This article may be of interest to you:

The blind men and the elephant: on meeting the problem of multiple truths in data from clustering and pattern mining perspectives
Arthur Zimek, Jilles Vreeken
in: Machine Learning, March 2013
http://link.springer.com/article/10.1007%2Fs10994-013-5334-y

It's somewhat philosophical, albeit with a slightly different orientation than what you were asking for AFAICT. But it may contain good pointers!

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