Dataset: We have 141,000 unique users, 1.6 million unique artists and 24.2 million user plays.

Topics:

###Alternating Least Squares (ALS):

Since there is no explicit information about users and the artists they like we search for implicit feedback data. It's important to not that in this case the data is rather sparse because some users may have only listened to a single artists and it's unlikely that a user has listened to a significant number of the possible number of artists.

###Latent Factor Model:

These models try to explain the observed interactions between users and products (artists in this case) through a relatively small number of unobserved, underlying reasons.

###Matrix Factorization Model:

User and product data are treated as a large matrix A where A[i][j] represents user i's play data for artist j. By factoring matrix A into the product of matrices X and Y we gain some insight at latent factors behind the data. We discover some size k that the two matrixes X and Y must share to be multipled.

It's important to note two things:

• Factorization is feasible because k is assumed to be small
• X and Y end up being dense through this process.

The small valued k could be interpreted as taste or genre in this context.

Factoring A into X and Y is impossible if we don't know X or Y so we start off ALS with completely randomized data for one matrix and solve for the other. If Y is random we minimize the absolute difference |A_iY(Y^TY)^-1 - X|. (Instead of computing inverses it's common to use QR decomposition.)

Now that we have some X we could solve for Y. If we proceeded in this fashion the algorithm guarantees convergence to a reasonable solution.