3

In this blog post Extraction of features from a given correlation matrix

the author claims:

the percentage of variance explained by the first PCA component and the average (absolute) correlation is the same thing

I think I understand what it means "variance explained", i.e. PCA and proportion of variance explained .

I can not understand how the proportion of highest eigenvalue and the average correlation provide the same information.

ABK
  • 396
  • 2
  • 17
  • 2
    I can find a sense in which the statement is true for $2\times 2$ correlation matrices, but not for larger ones. Here is `R` code to test it (showing my interpretation of the quotation, too). Here, `n` is the dimension of a random correlation matrix: `n – whuber Nov 30 '20 at 17:43

0 Answers0