Discounted Cumulative Gain

Definition

Discounted cumulative gain (DCG) is a measure of ranking quality in information retrieval.

$DC{G}_p=\sum _{i=1}^p\frac{{\text{rel}}_i}{{\log }_2(i+1)}$ $DC{G}_p=\sum _{i=1}^p\frac{2^{{\text{rel}}_i}-1}{{\log }_2(i+1)}$ where ${\text{rel}}_i$ is the graded relevance of the result at position $i$.

Normalized DCG

DCG is often normalized so that it is comparable across queries, giving Normalized DCG (NDCG). NDCG is DCG normalized by the maximum possible DCG of the result set.