I want to use scikit-learn NMF (from here) (or any other NMF if it does the job, actually).
Specifically, I have an input matrix (which is an audio magnitude spectrogram), and I want to decompose it.
I already have the W matrix pre-computed. How do I use a fixed W in sklearn.decompose.NMF? I haven't found any other question asking this.
I see that this method also mentions something similar in the fit parameter: "If False, components are assumed to be pre-computed and stored in transformer, and are not changed.". However, I am not sure how to make that transformer object.
This part of the code explains internal processing a bit.
It sounds you want to fix W. According to the code, you can only fix H, while optimizing W. That's not a problem, as you can just switch those matrices (invert their roles).
Doing this, the code says: use init='custom' and set update_h=False.
So in general i would expect usage to look like (based on the example here):
Untested!
import numpy as np
X = np.array([[1,1], [2, 1], [3, 1.2], [4, 1], [5, 0.8], [6, 1]])
fixed_W = np.array([[1,1,1],[1,1,1],[1,1,1],[1,1,1],[1,1,1],[1,1,1]) # size=3 just an example
# might break
fixed_H = fixed_W.T # interpret W as H (transpose)
from sklearn.decomposition import NMF
model = NMF(n_components=2, init='custom', H=fixed_H, update_H=False, random_state=0)
model.fit(X)
You probably want to switch your variables after solving again.
Edit: As mentioned in the comments, the untested code above won't work. We need to use the more low-level function available to do that.
Here is a quick hack (where i don't care much about the right preprocessing; transpose and co.) which should make you able to tackle your task:
import numpy as np
X = np.array([[1,1], [2, 1], [3, 1.2], [4, 1], [5, 0.8], [6, 1]])
fixed_W = np.array([[0.4,0.4],[0.2,0.1]]) # size=2 just an example
fixed_H = fixed_W.T # interpret W as H (transpose)
from sklearn.decomposition import NMF, non_negative_factorization
W, H, n_iter = non_negative_factorization(X, n_components=2, init='random', random_state=0)
print(W)
print(H)
print('error: ')
print(W.dot(H) - X) # just a demo, it's not the loss minimized!
W, H, n_iter = non_negative_factorization(X, n_components=2, init='custom', random_state=0, update_H=False, H=fixed_H)
print(W)
print(H)
print('error: ')
print(W.dot(H) - X)
Output:
[[ 0. 0.46880684]
[ 0.55699523 0.3894146 ]
[ 1.00331638 0.41925352]
[ 1.6733999 0.22926926]
[ 2.34349311 0.03927954]
[ 2.78981512 0.06911798]]
[[ 2.09783018 0.30560234]
[ 2.13443044 2.13171694]]
error:
[[ 6.35579822e-04 -6.36528773e-04]
[ -3.40231372e-04 3.40739354e-04]
[ -3.45147253e-04 3.45662574e-04]
[ -1.31898319e-04 1.32095249e-04]
[ 9.00218123e-05 -9.01562192e-05]
[ 8.58722020e-05 -8.60004133e-05]]
[[ 3. 0. ]
[ 5. 0. ]
[ 4.51221142 2.98707026]
[ 0.04070474 9.95690087]
[ 0. 12.23529412]
[ 0. 14.70588235]]
[[ 0.4 0.2]
[ 0.4 0.1]]
error:
[[ 2.00000000e-01 -4.00000000e-01]
[ -2.22044605e-16 -1.11022302e-16]
[ -2.87327549e-04 1.14931020e-03]
[ -9.57758497e-04 3.83103399e-03]
[ -1.05882353e-01 4.23529412e-01]
[ -1.17647059e-01 4.70588235e-01]]