MAP(Mean Average Precision)

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

MAP(Mean Average Precision)

MAP(Mean AveragePrecision)：单个主题的平均准确率是每篇相关文档检索出后的准确率的平均值。主集合的平均准确率(MAP)是每个主题的平均准确率的平均值。MAP 是反映系统在全部相关文档上性能的单值指标。系统检索出来的相关文档越靠前(rank越高)，MAP就可能越高。如果系统没有返回相关文档，则准确率默认为0。
例如：假设有两个主题，主题1有4个相关网页，主题2有5个相关网页。某系统对于主题1检索出4个相关网页，其rank分别为1, 2, 4,7；对于主题2检索出3个相关网页，其rank分别为1,3,5。对于主题1，平均准确率为(1/1+2/2+3/4+4/7)/4=0.83。对于主题2，平均准确率为(1/1+2/3+3/5+0+0)/3=0.7555。则MAP=(0.83+0.7555)/2=0.79。”

MRR是把标准答案在被评价系统给出结果中的排序取倒数作为它的准确度，再对所有的问题取平均。

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:

$\operatorname{AveP} = \frac{\sum_{r=1}^N (P(r) \times \mathrm{rel}(r))}{\mbox{number of relevant documents}} \!$

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:

$\mbox{P(r)} = \frac{|\{\mbox{relevant retrieved documents of rank r or less}\}|}{r}$

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