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What is the meaning of "eigenvalue > 1" criterion? I understand what eigenvalues and eigenvectors are.

This question is w.r.t. this link and this statement there:

By default, VARCLUS stops splitting when every cluster has only one eigenvalue greater than one, thus satisfying the most popular criterion for determining the sufficiency of a single underlying dimension.

I know it is a criterion for the number of clusters but how can one visualize and understand its meaning?

I have gone through this thread on principal component analysis but still do not understand it.

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Srikanth Guhan
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    This criterion (called "Kaiser rule") is for analyzing correlations only. Variance of every input variable is then 1. It is reasonable to retain only PCs which are "stronger" (have variance greater) than an individual input variable. In FA (unlike PCA) it is less obvious why it should be reasonable, still, we often decide to extract as many factors as there are components with eigenvalues >1. That is a heuristic rule, just one among several alternative ones, and not the best usually. – ttnphns Jun 16 '15 at 14:22
  • By saying "Variance of every input variable is then 1", do you mean that the variables are normalized? i.e. $\mu=0$ and $\sigma=1$ ? – Srikanth Guhan Jun 17 '15 at 08:08
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    Yes I do. Analyzing correlations _implies_ [standardized variables](http://stats.stackexchange.com/a/22520/3277). – ttnphns Jun 17 '15 at 08:36
  • Ok. And why is it less obvious in FA compared to PCA? Isn't it true that the latent factors should be explaining same or more than what the individial variables are explaining? – Srikanth Guhan Jun 17 '15 at 08:44
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    FA explains only the correlational, "common" portion of the variance. In every variable this portion is less than 1, the whole variance. So, it is realistic that a factor may have variance <1. The common portion of every variable is usually not known beforehand and it is dependent on the number of factors extracted. – ttnphns Jun 17 '15 at 09:16
  • @ttnphns: Would you consider making your comments an answer? They seem to have done the job! – Scortchi - Reinstate Monica Jun 18 '15 at 21:18

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