Fixed modes in non_negative_tucker_hals

[fosfrancesco]

Hi tensorly team,

I'm trying to run non negative tucker decomposition ( non_negative_tucker_hals) with fixed modes.
My goal would be:

1. run it on some 3-dimensional data D to obtain a decomposition D = [G; A, B, C]
2. fix A and run it again on some other data to obtain the new matrices G, B, and C (and of course the same A).

If I'm not mistaken, the parameter fixed_modes is there for this reason. So I would set it as fixed_modes = [2].
However, I can't find a way to input the "old" A. By looking at pull requests I think I need to use the init parameter, but I can't find the correct way to set it.

Here is how I would like my code to look (there is an "?" that need to be filled with correct values):

from tensorly.decomposition import non_negative_tucker_hals

m1 = np.random.random([10,15,20])
tensor_hals, error = non_negative_tucker_hals(a, rank = (3,4,5), return_errors= True)

m2 = np.random.random([10,15,20])
tensor_hals2, error2 = non_negative_tucker_hals(b,rank = (3,4,5), return_errors= True, fixed_modes = [2], init = ?)

Thank you for your help and your great work!

Francesco

[caglayantuna]

Hi @fosfrancesco ,

Thanks to your question, I realized a bug in non_negative_tucker_hals which doesn't work with fixed modes. I will work on it soon and inform you from here.

For the second part of your question, you should use TuckerTensor as init when you use fixed modes or factors (these names should be compatible as well). Here is an example by using your code and tucker decomposition:

from tensorly.decomposition import non_negative_tucker_hals, tucker
import numpy as np

m1 = np.random.random([10,15,20])
tensor_hals, error = non_negative_tucker_hals(m1, rank = (3,4,5), return_errors= True)

m2 = np.random.random([10,15,20])
tensor_hals2 = tucker(m2, rank=(3,4,5), fixed_factors= [1], init=tensor_hals)

By the way, tucker decomposition has no return_errors option that should be included.

Thanks,
Caglayan

[fosfrancesco]

Thank you very much for the fast answer, is it clear now!
And let me know when you have time to solve the issue, unfortunately, I really need the non-negativity for my application and I see that non_negative_tucker (without hals) does not support the fixed_modes.

Best,

Francesco

[caglayantuna]

Hello again,

Actually, non_negative_tucker_hals only fails when the last mode is fixed as parafac. So, in your fist question, it was 2 (last mode) and failed. There should be a warning about it or I have another idea to fix the last mode, maybe I can do a PR soon.

You can run the same example above with fixed_modes= [1] but I suggest you to use init=tensor_hals.tucker_copy() to avoid changes on tensor_hals.

Best,

Caglayan

[fosfrancesco]

Interesting! So if I am interested in fixing the third mode of m1, can I just transpose m1 (np.transpose(m1, (0,2,1))) and then use fixed_modes = [1]?

Will it be the same thing as fixing [2] on the untransposed matrix? I'm just starting working with those tensor transformations and I think this is correct, but I'm not 100% sure.

[cohenjer]

Exactly, you can use transpose beforehand. The last mode thing is a problem that comes from storing the results of the last updated mode to speed up computations of errors and such; we could get rid of it but nobody has the taken the time to do so I guess !

[fosfrancesco]

Thank you very much for your help. I will repay you with a lot of paper citations! And some contributions to the repo when I will have the time.