A simple recommender system

Here is an item-to-item version in which the utility matrix is Boolean: .

Recommender algorithm 1 is as follows. Given an input list of (i, j) pairs, representing purchases of items y_j bought by users x_i:

1. Initialize the utility matrix (u_ij) with m rows and n columns, where m is the number of users and n is the number of items.

2. For each pair (i, j) in the input list, set u_ij = 1.

3. Initialize the similarity matrix (s_jk) with n rows and n columns.

4. For each j = 1…n and each k = 1…n, set s_jk = s(u, v), the cosine similarity of the j^th column u and the k^th column v of the utility matrix.

5. For a given user-purchase pair (i, j) (that is, u_ij = 1):

   • Find the set S of items not bought by user i

   • Sort the items in S according to how similar they are to item j

6. Recommend the top n₁ elements of S, where n₁ is a specified constant much less than n.

To implement this algorithm, we need an input list of purchases. The program in Listing 9.2 generates a random list of pairs, where the pair...