# Discounted Cumulative Gain - Used by many web search companies - Graded relevance judgments as opposed to binary metrics like [[Precision and Recall]] - Emphasis on retrieving highly relevant documents - Two assumptions: - Graded relevance as a measure of the *usefulness or gain* from examining a document; hence the higher the better - The lower the *ranked position* of a document, the less useful it is for the user, since it is less likely to be examined - Therefore DCG is the total gain accumulated at a particular rank k: $ \mathrm{DCG} @ \mathrm{k}=\sum_{\mathrm{rank}}^{k} \frac{2^{r e l_{r}}-1}{\log _{2}(1+r)} $ - The numerator is the non-linear gain, having highly relevant document at the top matters much more than slightly relevant document at the top, so non-linear. - The denominator is the discount. ## Normalized DCG Normalizes DCG against the best possible DCG result (the perfect ranking) for the query - $0<=$ NDCG lt;=1$ - makes averaging easier for queries with different numbers of relevant documents --- ## References