Recommender Systems by Charu C. Aggarwal

Author:Charu C. Aggarwal
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(7.18)

It is also possible to define the average reciprocal hit-rate for a recommended list of size L by adding only those utility values for which v j  ≤ L.

(7.19)

One quirk of the average reciprocal hit-rate is that it is typically used when the value of | I u  | is exactly 1, and when the value r uj of the corresponding (hidden) item j ∈ I u is always 1. Therefore, there is exactly one hidden item for each user, and the user has always bought or clicked on this item. In other words, the average reciprocal hit-rate rewards the utility (in a rank-reciprocal way) for recommending the single correct answer at a high position on the recommended list. This was the setting in which this measure was introduced [181], although one can generalize it to arbitrary settings in terms of the number of hidden items and explicit-feedback settings. The aforementioned expression provides this generalized definition because one can use a set I u of arbitrary size in an explicit feedback setting. The global ARHR value is computed by averaging this value over the m users:

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