Non Negative Matrix Factorization: How to predict values for a new entry?

Question

My current understanding:
I have tried reading a few papers and links regarding NMF. It all talks about how we can split a MxN matrix into MxR and RxN matrices(R

Question:
I have a list of users(U) and some assignments(A) for each user. Now I split this matrix(UxA) using NMF. I get 2 Matrices UxR and RxA. How do I use these to predict what assignments(A') a new user(U') must have?

Any help would be appreciated as I couldn't understand this after trying to search for the answer.

Side question and opinion based:
Also if anyone can tell me with their experience, how do they chose R, specially when the number of assignments are in the order of 50,000 or perhaps a hundred thousand. I have been trying these with the scikit-learn library

Edit: This can simply be done using model.inverse_transform(model.transform(User'))

Answer 1

You can try think this problem as recommender. you want to approximate decompose matrix X into two nonnegative matrix U and V.

see https://cambridgespark.com/content/tutorials/implementing-your-own-recommender-systems-in-Python/index.html

For pyothn scikit-learn, you can use: http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.NMF.html

from sklearn.decomposition import NMF
model = NMF(n_components=2, init='random', random_state=0)
W = model.fit_transform(X)
H = model.components_

Where X is the matrix you want to decomose. W and H is the nonnegative factor

To predict what assignments(A') a new user(U'), you just use WH' to complete the maitrx