matrix-factorization | matrix factorization for recommender system | Recommender System library

See here a Python implementation of NMF decomposition of the MNIST dataset, with clear steps & visualizations, and access to H, W and X datasets in the code.

https://bitbucket.org/leenremm/nmf_mnist

Your linked notebook is creating a 'blank' sparse matrix, and setting selected elements from data it reads from a csv.

A simple example of this:

This might not be considered as an answer.

Of course you don't need to pass the missing ratings whether it's implicit or explicit.

One of the strength of spark is computing your prediction matrix using sparse matrices representation.

If you wish to know a little bit more about sparse matrices, you can check the following link :

What are sparse matrices used for ? What is its application in machine learning ?

Disclaimer: I'm the author of the answer in that link.

In scikit-learn, NMF does more than simple matrix multiplication: it optimizes!

Decoding (inverse_transform) is linear: the model calculates X_decoded = dot(W, H), where W is the encoded matrix, and H=model.components_ is a learned matrix of model parameters.

Encoding (transform), however, is nonlinear : it performs W = argmin(loss(X_original, H, W)) (with respect to W only), where loss is mean squared error between X_original and dot(W, H), plus some additional penalties (L1 and L2 norms of W), and with the constraint that W must be non-negative. Minimization is performed by coordinate descent, and result may be nonlinear in X_original. Thus, you cannot simply get W by multiplying matrices.

NMF has to perform such strange calculations because, otherwise, the model may produce negative results. Indeed, in your own example, you could try to perform transform by matrix multiplication

To get a prediction resembling "probabilities" you could use --loss_function logistic --link logistic. Be aware that in this single-label setting your probabilities risk tending to 1.0 quickly (i.e. become meaningless).

• Working with a single label is problematic in the sense that there's no separation of the goal. Eventually the learner will peg all predictions to 1.0. To counter that - it is recommended to use --noconstant, use strong regularization, decrease the learning rate, avoid multiple passes, etc. (IOW: anything that avoids over-fitting to the single label)
• Even better: add examples where the user hasn't bought/clicked, they should be plentiful, this will make your model much more robust and meaningful.
• There's a better implementation of matrix factorization in vw (much faster and lighter on IO for big models). Check the --lrq option and the full demo under demo/movielens in the source tree.
• You should pass the training-set directly to vw to avoid Useless use of cat