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Q-measure is a graded-relevance version of the well-known Average Precision. Let R denote the number of known relevant documents for a topic; let gainl denote the gain value for a document of relevance level l: for example, let it be 3 for a highly relevant document, 2 for a relevant document, and 1 for a partially relevant document. For a given ranked list of documents, let I(r) = 0 if the document at rank r is nonrelevant, and I(r) = 1 otherwise; then \(C(r)=\sum _{k=1}^{r}I(k)\): the number of relevant documents within top r. Note that Precision at r is given by C(r)∕r. Let g(r) = gainl if the document at rank r is l-relevant and let g(r) = 0 otherwise; let the cumulative gain be \(\textit {cg}(r)=\sum _{k=1}^{r}g(k)\). Define an ideal ranked list for the topic by sorting the R relevant documents by relevance level; let cg∗(r) denote the cumulative gain at r for the ideal list. Then Q-measure is defined as:
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Sakai, T. (2018). Q-Measure. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_80616
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DOI: https://doi.org/10.1007/978-1-4614-8265-9_80616
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-8266-6
Online ISBN: 978-1-4614-8265-9
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