Recommender Systems

The two primary models are as follows:

1. Prediction version of problem: The first approach is to predict the rating value for a
user-item combination. It is assumed that training data is available, indicating user
preferences for items. For m users and n items, this corresponds to an incomplete
m × n matrix, where the specified (or observed) values are used for training. The
missing (or unobserved) values are predicted using this training model. This problem
is also referred to as the matrix completion problem because we have an incompletely
specified matrix of values, and the remaining values are predicted by the learning
algorithm.

2. Ranking version of problem: In practice, it is not necessary to predict the ratings of
users for specific items in order to make recommendations to users. Rather, a merchant
may wish to recommend the top-k items for a particular user, or determine the top-k
users to target for a particular item. The determination of the top-k items is more
common than the determination of top-k users, although the methods in the two cases
are exactly analogous. Throughout this book, we will discuss only the determination of
the top-k items, because it is the more common setting. This problem is also referred
to as the top-k recommendation problem, and it is the ranking formulation of the
recommendation problem.