From the rating matrix in the previous section, we see that every user can be represented as a j-dimensional vector where the kth dimension denotes the rating given by that user to the kth item. For instance, let 1 denote a like, -1 denote a dislike, and 0 denote no rating. Therefore, user B can be represented as (0, 1, -1, -1). Similarly, every item can also be represented as an i-dimensional vector where the kth dimension denotes the rating given to that item by the kth user. The video games item is therefore represented as (1, -1, 0, 0, -1).
We have already computed a similarity score for like-dimensional vectors when we built our content-based recommendation engine. In this section, we will take a look at the other similarity measures and also revisit the cosine similarity score in the context of the other scores.
