Intuitively, the purpose of the positive coefficients constraint is to allow for the interpretation as a mixture (admixture?) of components. This constraint giv

Intuitively, the purpose of the positive coefficients constraint is to allow for the interpretation as a mixture (admixture?) of components. This constraint gives the nice properties of W. In principle there is no reason why you wouldn't allow negative coefficients in H, but if you want the W to learn additive components, then you need the non-negative constraint.