Handling `missing data`

[nipunbatra]

Thanks ton for the wonderful package! I was wondering if there is some way in which missing data can be handled? The trivial application being MovieLens like dataset. I was wondering if instead of the usual 0 rating for missing entries in the matrix, we could just let those entries be np.NaN?

[kimjingu]

Thank you for the question. Totally agree that it would be very nice to be able to handle missing data. This means that the objective would need to be weighted sum of squares where no weight is given to unobserved values. Supporting the minimization of weighted sum of squares is conceptually feasible but would need some amount of restructuring of the current implementation.

[nipunbatra]

I am wondering if this can be done something like (say for an ALS implementation):

cost = |A[mask] -A_pred[mask]|_F instead of cost = |A -A_pred|_F.

Here, mask is simply a boolean matrix telling us where the entries exist.

[kimjingu]

Sure, maybe you could derive a few more steps on how A_pred can be updated? Have you tried implementing it?

[nipunbatra]

To be honest, I am not sure. However, I thought that maybe we could brainstorm on predicting A_pred using NNLS initially?

[nipunbatra]

I have written the following code to handle missing data using NNLS. Can you please confirm if this looks okay? I am not sure how other algorithms would be able to incorporate missing data.

I was wondering if you'd be able to suggest how to use NNLS for NTF, as I am doing for NMF?