NMF buys interpretability with error

NMF minimizes the same ‖A − B‖_F as the truncated SVD, but subject to W, H ≥ 0.

That extra constraint must be worse on error — Eckart–Young already proved the SVD is optimal — and it is chosen anyway, because the components come out as parts you can name.

This is the clearest example of the section’s organizing idea: a factorization is a constrained optimization, and you pick the constraint that matches what you need, not the one that minimizes the number.