Negative Latent Factors in Factorization Machines

Question

I'm studing a specific implementation of a recommendation system leveraging on a factorization machine algorithm. For each person_id and item_id combination, I have an implicit rating of 1 or 0 depending on if the user downloaded the content or not. In the base model, I have just utilized as input variables the person_id and the item_id. I selected a latent factor number equal to 5. In the model output, some of the 5 the latent factors associated to some person_id and item_id are negative, and some predictions of the rating for the combination person_id/item_id are negative too. I have searched for some theoretical explanations but not found much material, so here I am.

How a negative latent factor can be explained in this setting? Being the training dataset provided with the target variable equal to 1 or 0, how the model end up with negative predictions for the implicit rating?

Answer 1

Found after some digging many concepts related to Non-Negative Matrix Factorization, which if properly setup constrain a FM algorith to come up with non negative factors (and therefore predictions.). Many useful material here:

• https://en.wikipedia.org/wiki/Non-negative_matrix_factorization
• https://towardsdatascience.com/parts-based-learning-by-non-negative-matrix-factorisation-1279ffd29618