confusing: How to obtain the AUC for implicit feedback recommender system?

Question

I am confusing how to calculate the AUC (area under the curve) for implicit feedback recommender system. Since it is implicit data, that means we just know the positive entries while we do not know the negative entries. For evaluating such recommender system, recall-based metric (such as MPR, mean percentile ranking) is ok. But AUC calculation should also need the negative entries, that is unknown in fact for implicit data. But I notice some papers also showed the AUC, can you help me or give me a hint about how to calculate AUC for implicit data-based recommender system?

How to obtain the negative entries?

Answer 1

The AUC Curve is calculated from the True Positive and False Positive rates. True positives are the items that the recommender recommends for a given user and are as well in the test set for a given user. False positives are items recommended by the algorithm for a given user and are missing in the user's test vector.