Building a recommendation engine using k-means. A set of N users of a music-streaming app listens to songs from a library of n songs over some period (say, a month). We describe user is listening habits by her playlist vector, which is the n-vector p_i defined as: , for j = 1, ..., n. (Note that p_i is an n-vector, while (p_i)_j is a number. You can assume that if a user listens to a song, she likes it.

Your job (say, during a summer internship) is to design an algorithm that recommends to each user 10 songs that she has not listened to, but might like. (You can assume that for each user, there are at least 10 songs that she has not listened to.)

To do this, you start by running k-means on the set of playlist vectors p₁, ..., p_N (Its not relevant here, but a reasonable choice of k might be 100 or so.) This gives the centroids z₁, ..., z_k, which are n-vectors.

Now what do you do? You can explain in words; you do not need to give a formula to explain how you make the recommendations for each user.

S1 notandi i has played song i (pi)) = 3 o notandi i has not played song i S1 notandi i has played song i (pi)) = 3 o notandi i has not played song