Their first recommender is a user-based CF system i.e. the score given to a new recommendation of Muse for user Jim is a weighted average over all the scores (ratings, scrobbles, etc.) for users who already listen to Muse, and the weights are similarities computed between Jim and each of Muse's fans.

Yuan et al. start with a baseline CF recommender in which the similarity between users is based on cosine distance between their vectors of artist scrobbles. For reasons that aren't obvious to me, the scrobble counts are first mapped to binary values, e.g. 1 if a user has scrobbled Muse three or more times, 0 otherwise. In their first experimental recommender, these similarities are augmented by a weighted combination of similarities based on friend and group membership relationships. The relationship similarities are also computed as cosine distances between binary vectors, so the friendship similarity between two users expresses the extent to which they have friends in common, and likewise for group membership.

The second experimental system is a graph-based recommender, built on a graph of user, artist and group nodes. The graph starts with the obvious edges between users and the artists they listen to, and the groups they belong to. Then edges are added between pairs of users whose relationship similarities are more than some threshold, so each user is connected to other users with similar friends or belonging to similar groups as well as to their 'real' friends. Like the binary CF vectors in the first system, the edge weights are all set to 1. Finally user-user similarity scores are extracted from the graph using a Laplacian matrix pseudoinverse algorithm: in practice the computation required is similar to inverting a matrix containing concatenated artist, friend and group vectors for each user.

After these nice simple suggestions for combining social relationships and CF, the experiments themselves are a bit of a disappointment, mainly because the dataset they use contains only 1000 artists and users. The evaluation metrics are precision, recall and f-value over the top few recommendations, where a recommendation is considered correct if the user actually scrobbled the reommended artist at least three times. In the CF recommender, using weights that seem to be rather highly fitted to the small dataset, there is a 2-3% improvement in f-value over the top five recommendations. The graph recommender shows an 8% improvement, but they don't give baseline results from a graph not including the social relationships, so it's not clear whether this is due to the extra social information or just the different algorithm.

In fact using such a small dataset raises all sorts of problems in interpreting the results:

- it's hard to tell if absolute values are good or bad
- is it sensible to evaluate the top-5 recommendations from a pool of only 1000 artists?
- are the improvements significant?
- are the various parameters overfitted?
- does the graph method scale?

It makes me suspect that IBM are just playing in the recommender space, while others are clearly serious about it.

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