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The number of Eigenvectors selected after a PCA transformation can be done in several ways. One such method is using the total amount of variance explained by each principal component. That is, select the top $n$ Eigenvectors such that the cumulative variance explained by them reaches a $p$ (e.g., 99%).

This notion was applied in my paper. However, the reviewers require an analysis on how I came to this decision or a relevant citation perhaps.

I learnt this through Andrew Ng's Machine Learning course in Coursera, but I'm not able to find a solid published reference to this anywhere.

Can someone please provide an apt citation that states this concept or analyses it in any way?

Ébe Isaac
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    Jolliffe's [Principal Component Analysis](http://www.springer.com/us/book/9780387954424) is canonical reference on the matter; this should suffices for almost all cases. – usεr11852 Jun 08 '17 at 18:50
  • @usεr11852 Did that already, but cannot find the direct quote on a shallow search. Can you specify a page number ref, please? – Ébe Isaac Jun 08 '17 at 18:51
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    The literature I am familiar with does not generally support such a procedure. It points out there are *many* different procedures for selecting the PCs: look for the inflection in the Scree Plot; pick all with eigenvalues above 1; etc--and that most of these have no universal justification. You therefore might be better off explaining *your* reason for applying this procedure. (And no, stating you were taught it is not a reason. A true reason appeals to theory and analytical objectives.) Such an explanation would be the most relevant and meaningful. – whuber Jun 08 '17 at 19:01
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    Sorry; I probably be misunderstood what you are asked. I (mis)interpreted it as asking for a reference for why $k$ number of components explained $X%$ of variance. If it is a case of choosing $k$, just look at some of the reference in cited one of the threads [here](https://stats.stackexchange.com/questions/44060) or [here](https://stats.stackexchange.com/questions/33917). As whuber mentioned in a paper we want to say "why we picked $k$" (unless it a PCA methodological paper but that's another ball-game). – usεr11852 Jun 08 '17 at 19:54

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The technical term for what you describe in your original post is Kaiser's criterion. I spot-checked several articles, and none of them provide a specific citation for this term.

Building from @whuber's answer, I would strongly suggest you use multiple methods for determining how many factors to retain. I recommend Velicer's MAP test and parallel analysis (for more info refer here and see O'Connor, 2000).

HappySnowman
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