NDCG

Discounted cumulative gain (DCG) is a measure of ranking quality. In information retrieval, it is often used to measure effectiveness of web search engine algorithms or related applications. Using a graded relevance scale of documents in a search-engine result set, DCG measures the usefulness, or gain, of a document based on its position in the result list. The gain is accumulated from the top of the result list to the bottom, with the gain of each result discounted at lower ranks.

Two assumptions are made in using DCG and its related measures.

DCG originates from an earlier, more primitive, measure called Cumulative Gain.

Cumulative Gain (CG) is the predecessor of DCG and does not include the position of a result in the consideration of the usefulness of a result set. In this way, it is the sum of the graded relevance values of all results in a search result list. The CG at a particular rank position ${\displaystyle p}$ is defined as:

Where ${\displaystyle rel_{i}}$ is the graded relevance of the result at position ${\displaystyle i}$.

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