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Questions in respect to rotation post-PCA have been answered before -> its all in the hands of the researcher... Same answer to the question if rotation (orthogonal or not) makes sense before plugging the components into a cluster analysis?

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You should definately make your question self contained and more clear to get better/any answers. –  bayerj Mar 4 '13 at 20:23
    
Welcome to the site, @user21537. At present it is not clear exactly what you are asking, & thus what exactly would be an answer. It might help if you could provide us w/ more details about your situation, your data & your goals; you may find the following blog post helpful in formulating your question: How to ask a statistical question. If not, this Q may end up being closed. –  gung Mar 4 '13 at 20:54
    
Thanks for the greetings! –  nafets Mar 5 '13 at 17:56
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I specifically wasn't trying to be specific. It's more of a rules of thumb question. Clearly interpretation of PCA components may be improved by rotation, but is that potential improvement inherited by more sensible clustering? E.g. in my dataset I've rotated orthogonally and then saw no difference in the pattern of hierarchical clustering thereafter compared to the unrotated solution -> is that the rule then and/or are there exceptions. –  nafets Mar 5 '13 at 18:02
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1 Answer 1

If the PCA is only being done as a pre-processing step and the diagnostics of the PCA are ignored and the PCA is not used to interpret the resulting cluster analysis then it makes no sense to rotate the PCA. However, rotating it isn't going to invalidate the cluster analysis in any way.

However, if it is important to interpret the clusters then it is often useful to rotate the components as you can then interpret the loadings and the other diagnostics and decide how many components to use in the cluster analysis. Further, when you go down this path you can quickly intepret the clusters by evaluating how they differ in terms of the means of the components.

I would not be considering any non-orthogonal rotations. Such rotations are typically only used in situations where researchers are keenly interested in the interpretation of the PCA and have various theoretical beliefs regarding the underlying structure of the data (e.g., if developing psychometric tests). In situations where it is just a pre-processing step non-orthogonal rotations become problematic (e.g., perhaps they will create a structure in the data that is then identified by the cluster analysis). At the risk of making up a number, 99.99% of PCA applications by experienced researchers that are rotated do so using Varimax.

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I wonder whether that percentage of Varimax rotations is due to it being the more venerable technique and being the default used in many stats software packages rather than a considered choice. –  rpierce Mar 6 '13 at 2:34
    
Again to make up some more numbers, the vast majority of PCAs where people are interested in interpreting the outputs (as opposed to pre-processing data) are done in SPSS and SPSS does not have Varimax as the default. Nevertheless I accept your general point and would add a slightly more cynical aspect to it: analyses done using PCA are pretty rubbery anyway and there is generally no coherent way to validate the resulting models other than judgment so inevitably the methodologies that people routinely employ reflect preference and memes rather than survival of the fittest. –  Tim Mar 6 '13 at 6:41
    
@Tim 99.9% sounds like a rule of thumb ;) I can perfectly follow your explanation - thanks! –  nafets Mar 6 '13 at 7:52
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