正規化割引累積利得 (NDCG) は、一般的に使用される指標です 情報検索 and レコメンデーションシステム to evaluate the quality of ranked lists. NDCG takes into account the position of relevant documents in the ranked list, emphasizing the importance of higher-ranked items. The metric is especially useful in scenarios where the relevance of items is not binary but graded (e.g., on a scale from 0 to 3).
NDCGの計算は二つの主なステップを含みます：まず、 computing the 累積利得（CG）, which sums the relevance scores of the retrieved items based on their ranks. The second step is applying a 割引関数, often logarithmic, to reduce the weight of lower-ranked items, reflecting the principle that users are more likely to engage with items presented earlier in the list.
CGを正規化するために、NDCGは 理想割引累積利得（IDCG）を使用します, which represents the maximum possible gain for an ideal ranking アイテムの順位付けのために。最終的なNDCGスコアは次のように計算されます：
NDCG = (DCG) / (IDCG)
This normalization ensures that NDCG values range from 0 to 1, making it easier to compare the effectiveness of different ランキングアルゴリズム. A higher NDCG score indicates better retrieval performance, as it means that relevant items are ranked higher.
NDCG is widely used in various applications, including search engines, recommendation systems, and 機械学習 models, to assess how well a system meets user expectations and retrieves pertinent information.