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

There is no correct answer, it is somewhere between 1 and n.

Think of a principal component as a street in a town you have never visited before. How many streets should you take to get to know the town?

Well, you should obviously visit the main street (the first component), and maybe some of the other big streets too. Do you need to visit every street to know the town well enough? Probably not.

To know the town perfectly, you should visit all of the streets. But what if you could visit, say 10 out of the 50 streets, and have a 95% understanding of the town? Is that good enough?

Basically, you should select enough components to explain enough of the variance that you are comfortable with.