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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.

  1. How a negative latent factor can be explained in this setting?
  2. 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?

Many thanks for any hints or material bests

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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:

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