MAP(Mean Average Precision)

MAP(Mean Average Precision)：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)/5=0.45。则MAP= (0.83+0.45)/2=0.64。”

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 whole list of documents returned by the system. For systems that return a ranked sequence of documents, it is desirable to also consider the order in which the returned documents are presented. Average precision emphasizes ranking relevant documents higher. It is the average of precisions computed at the point of each of the relevant documents 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 the area under the Precision-Recall curve.

Note that the denominator (number of relevant documents) is the number of relevant documents in the entire collection, so that the metric reflects performance over all relevant documents, regardless of a retrieval cutoff. See:.

^ Turpin, Andrew; Scholer, Falk (2006). "User performance versus precision measures for simple search tasks". Proceedings of the 29^th Annual international ACM SIGIR Conference on Research and Development in information Retrieval_r(Seattle, Washington, USA, August 06-11, 2006) (New York, NY: ACM): 11–18. doi:10.1145/1148170.1148176

MAP(Mean Average Precision)：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)/5=0.45。则MAP= (0.83+0.45)/2=0.64。”