Explicit matrix factorization

When we deal with data that consists of preferences of users, which are provided by the users themselves, we refer to explicit preference data. This includes, for example, ratings, thumbs up, likes, and so on that are given by users to items.

We can take these ratings and form a two-dimensional matrix with users as rows and items as columns. Each entry represents a rating given by a user to a certain item. Since, in most cases, each user has only interacted with a relatively small set of items, this matrix has only a few non-zero entries, that is, it is very sparse.

As a simple example, let's assume that we have the following user ratings for a set of movies:

Tom: Star Wars, 5

Jane: Titanic, 4

Bill: Batman, 3 ...

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