I know for PCA, it's true that the first N eigenvectors have N greatest variance.
But I'm not sure whether that's also true for NMF(Non-negative Matrix Factorization). For example, this method(Standard Nonnegative Matrix Factorization (NMF) [Lee2001], [Lee1999].): http://nimfa.biolab.si/nimfa.methods.factorization.nmf.html
And are there articles that write about how to calculate the variance of first N eigenvectors? What is the best k(k means counts of eigenvector) for dimension reduction?