from： http://blog.sina.com.cn/s/blog_662234020100pozd.html

MAP(Mean?Average?Precision)

MAP(Mean AveragePrecision)：單個主題的平均準確率是每篇相關文檔檢索出后的準確率的平均值。主集合的平均準確率(MAP)是每個主題的平均準確率的平均值。MAP 是反映系統(tǒng)在全部相關文檔上性能的單值指標。系統(tǒng)檢索出來的相關文檔越靠前(rank越高)，MAP就可能越高。如果系統(tǒng)沒有返回相關文檔，則準確率默認為0。
例如：假設有兩個主題，主題1有4個相關網頁，主題2有5個相關網頁。某系統(tǒng)對于主題1檢索出4個相關網頁，其rank分別為1, 2, 4,7；對于主題2檢索出3個相關網頁，其rank分別為1,3,5。對于主題1，平均準確率為(1/1+2/2+3/4+4/7)/4=0.83。對于主題2，平均準確率為(1/1+2/3+3/5+0+0)/3=0.7555。則MAP=(0.83+0.7555)/2=0.79。”

MRR是把標準答案在被評價系統(tǒng)給出結果中的排序取倒數作為它的準確度，再對所有的問題取平均。

Wiki

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,andP(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 performanceversus precision measures for simple search tasks". Proceedingsof the 29^th Annual international ACM SIGIR Conference onResearch and Development in information Retrieval_r(Seattle,Washington, USA, August 06-11, 2006) (New York, NY: ACM):11–18.doi:10.1145/1148170.1148176

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