I have been comparing dimensionality reduction methods, while performing KPCA, I didn't know what number of PCs I should retain, how many to take and decide : "there it is, this is the new reduced data".

In normal PCA, I used the Kaiser's rule on the eigenvalues, dropping everything under the average eigenvalue. PCA cut with Kaiser's rule

But with KPCA, everything is under the average eigenvalue will give me way too much Principal components, even more than the original data. KPCA eigenvalues

I know that the stopping criteria should depend on the datasets , but I barely know the datasets used for the test, and I would like some rule or criteria that works generally , like for every case

  • $\begingroup$ There is no general rule; it depends on the problem and your goals. This is also true for other forms of dimensionality reduction, including regular PCA. The Kaiser rule is not a great practice (e.g. see here). $\endgroup$
    – user20160
    Jan 26 at 2:54

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