# D-Measure

**DOI:**https://doi.org/10.1007/978-1-4614-8265-9_80620

## Definition

*D-measure* is a family of evaluation measures for *diversified search*, where we have a set of known *intents* (a.k.a. *subtopics*) {*i*} for a given topic *q* and the *intent probabilities**Pr*(*i*|*q*), such that ∑_{i}*Pr*(*i*|*q*) = 1. It is assumed that *per-intent* graded relevance assessments are also available for the topic and that the *gain value* for each document of relevance *l* with respect to a particular intent is given by *gain*_{l}. For example, let the per-intent gain be 3 for a highly relevant document, 2 for a relevant document, and 1 for a partially relevant document. Given a ranked list, let *g*_{i}(*r*) = *gain*_{l} if the document at rank *r* is *l*-relevant to intent *i*, and *g*_{i}(*r*) = 0 otherwise. The *global gain* at *r* is defined as *GG*(*r*) =∑_{i}*Pr*(*i*|*q*)*g*_{i}(*r*). An *ideal list* for diversified search is defined by sorting all known relevant documents by the global gain; the global gain at rank *r* in the ideal list is denoted by *GG*^{∗}(*r*). Then, any graded relevance evaluation measure computed based on *GG*(*r*) and *GG*^{∗}(*r*)...