  Conventional collaborative filtering techniques treat a top-n recommendations
problem as a task of generating a list of the most relevant items. This
formulation, however, disregards an opposite - avoiding recommendations with
completely irrelevant items. Due to that bias, standard algorithms, as well as
commonly used evaluation metrics, become insensitive to negative feedback. In
order to resolve this problem we propose to treat user feedback as a
categorical variable and model it with users and items in a ternary way. We
employ a third-order tensor factorization technique and implement a higher
order folding-in method to support online recommendations. The method is
equally sensitive to entire spectrum of user ratings and is able to accurately
predict relevant items even from a negative only feedback. Our method may
partially eliminate the need for complicated rating elicitation process as it
provides means for personalized recommendations from the very beginning of an
interaction with a recommender system. We also propose a modification of
standard metrics which helps to reveal unwanted biases and account for
sensitivity to a negative feedback. Our model achieves state-of-the-art quality
in standard recommendation tasks while significantly outperforming other
methods in the cold-start "no-positive-feedback" scenarios.
