How many principal components to take?

Question

I know that principal component analysis does a SVD on a matrix and then generates an eigen value matrix. To select the principal components we have to take only the first f

Answer 1

I highly recommend the following paper by Gavish and Donoho: The Optimal Hard Threshold for Singular Values is 4/sqrt(3).

I posted a longer summary of this on CrossValidated (stats.stackexchange.com). Briefly, they obtain an optimal procedure in the limit of very large matrices. The procedure is very simple, does not require any hand-tuned parameters, and seems to work very well in practice.

They have a nice code supplement here: https://purl.stanford.edu/vg705qn9070