How to extract features from nonstationary signal using SVD (singular value decomposition)?
What you're describing is a spectrum estimation based on signal representation in a vector space spanned by eigenvectors of a particular matrix generated from your signal observation.

That reminds me extremely much of MUSIC, and ESPRIT. I think the best way to go here is to read up on spectral estimation using MUSIC, which is based on the idea that there's an autocovariance matrix (which can be easily estimated by the dyadic product of a receive signal vector with itself, for example), and that autocovariance matrix can, using an EVD (which is a special case of the SVD for quadratic matrices), be diagonalized like you do it, into a an upper, lower and a diagonal matrix. Using the magnitudes of the eigenvalues (which happen to be the entries of the diagonal matrix), you can select the eigentvectors to span a sub-space that only contains autocovariance Eigenvectors (i.e. periodicities!) that are actually in the signal; the energy in the complementary sub-space is pretty much only noise.

Using that technique, you can directly get a function that you can sample to get a pseudospectrum (MUSIC), or through elegant rotations, the set of strongest frequencies in the signal (ESPRIT).

So, I don't get the full context of the "Eigenvectors that maximize the mean", but maybe you don't have to – you can walk on the shoulders of other SVD-based spectral estimation papers, and maybe that'll help you understand the one you're currently reading (or you just build a scalogram matrix and hit it with MUSIC as if it was an autocovariance matrix estimate, and see what happens – I love just experimenting with algorithms :) ).