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?

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    $\begingroup$ Jolliffe's Principal Component Analysis is canonical reference on the matter; this should suffices for almost all cases. $\endgroup$
    – usεr11852
    Jun 8, 2017 at 18:50
  • $\begingroup$ @usεr11852 Did that already, but cannot find the direct quote on a shallow search. Can you specify a page number ref, please? $\endgroup$
    – Ébe Isaac
    Jun 8, 2017 at 18:51
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    $\begingroup$ 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. $\endgroup$
    – whuber
    Jun 8, 2017 at 19:01
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    $\begingroup$ 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 or here. 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). $\endgroup$
    – usεr11852
    Jun 8, 2017 at 19:54

1 Answer 1


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).

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    $\begingroup$ % of variance explained isn't Kaiser's criterion $\endgroup$
    – ttnphns
    Jun 9, 2017 at 15:48

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