A recommendation system keeps a log of what recommendations have been made to a particular user and whether that user accepts the recommendation. It's like
user_id item_id result 1 4 1 1 7 -1 5 19 1 5 80 1
where 1 means the user accepted the recommendation while -1 means the user did not respond to the recommendation.
Question: If I am going to make recommendations to a bunch of users based on the kind of log described above, and I want to maximize MAP@3 scores, how should I deal with the implicit data (1 or -1)?
My idea is to treat 1 and -1 as ratings, and predict the rating using factorization machines-type algorithms. But this does not seem right, given the asymmetry of the implicit data (-1 does not mean the user does not like the recommendation).
Edit 1 Let us think about it in the context of a matrix factorization approach. If we treat -1 and 1 as ratings, there will be some problem. For example, user 1 likes movie A which scores high in one factor (e.g. having glorious background music) in the latent factor space. The system recommends movie B which also scores high in "glorious background music", but for some reason user 1 is too busy to look into the recommendation, and we have a -1 rating movie B. If we just treat 1 or -1 equally, then the system might be discouraged to recommend movie with glorious BGM to user 1 while user 1 still loves movie with glorious BGM. I think this situation is to be avoided.