Protein profile by NMF

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Protein profile by NMF

Marcal Plans
Hi community,
I have an interesting challenge that i think that it can be resolved using
NMF.
I have a total of 52 product with different protein profiles. I would like
to make two protein premixes (two unique profiles) to create all the SKU
using different concentrations of them (mixing). I have tried
the  following code and it partially works. The main problem is that the
levels that i have in the spec are the minimum protein concentrations
[minimum guarantee].
The solution that I got is the average that minimize the error, but with
this profile of proteins and concentrations I have profiles that do not
reach the minimum requirements. We can overdose, but we cannot under dose.

Code:

Data=read.table("clipboard", header=T, sep="\t", dec=".")
res=nmf(Data[,-1],2, nrun=30, seed=12345)
C=as.matrix(.coef(res)*100000)
S=as.matrix(basis(res)/100000)

#write.csv(S%*%C, "Test1.csv")
DD=(Data[,-1]-S%*%C)/(Data[,-1])*100+100
summary(DD)

Is there any way to add some restrictions to the NMF? for example W%*%H>
Data
Is there a better algorithm to factorize this data set?

Thank you so much for your help!
Cheers,
Marcal
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