Precision and recall are single-value metrics based on the wholelist of documents returned by the system. For systems that return aranked sequence of documents, it is desirable to also consider theorder in which the returned documents are presented. Averageprecision emphasizes ranking relevant documents higher. It is theaverage of precisions computed at the point of each of the relevantdocuments in the ranked sequence:
where r is the rank, N the number retrieved,rel() a binary function on the relevance of a given rank,and P(r) precision at a given cut-off rank:
This metric is also sometimes referred to geometrically as thearea under the Precision-Recall curve.
Note that the denominator (number of relevant documents) is thenumber of relevant documents in the entire collection, so that themetric reflects performance over all relevant documents, regardlessof a retrieval cutoff. See:.
^Turpin, Andrew; Scholer, Falk(2006). "User performance versus precision measures for simplesearch tasks". Proceedings of the 29th Annualinternational ACM SIGIR Conference on Research and Development ininformation Retrieval_r(Seattle, Washington, USA, August 06-11,2006) (New York, NY: ACM): 11–18. doi:10.1145/1148170.1148176
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