Why not flatten first?

Flattening preserves the numerical entries but can hide the meaning carried by separate modes.

The fluorescence-unmixing example makes the difference measurable:

• CP recovers the true component amounts at correlation 1.00.
• Flatten-then-SVD reaches only mean |corr| ≈ 0.536.
• The SVD representation can produce negative amount directions, even though a physical concentration cannot be negative.

Flattening is not necessarily wrong. The problem appears when we fuse two modes whose separate meaning was precisely the information we wanted to interpret.