正規化割引累積利得（NDCG）指標
その 正規化割引累積利得 (NDCG) metric is widely used in 情報検索 and レコメンデーションシステム to evaluate the effectiveness of algorithms in ranking items according to their relevance to a user’s query. NDCG takes into account both the position of an item in the ranked list and the relevance of that item, making it particularly useful when the items have varying levels of importance.
NDCG is calculated in two main steps: first, the Discounted Cumulative Gain (DCG) is computed, which sums the relevance scores of the retrieved items, discounted by their rank position. The formula for DCG at rank p is given by:
DCG_p = rel_1 + Σ (rel_i / log2(i + 1)), for i = 2 to p
where rel_i is the 関連性スコア of the item at rank i.
次に、NDCGはDCGスコアを理想的なDCG（IDCG）で割ることで正規化されます。理想的なDCGは、アイテムの関連性に基づく最良のランキングリストのDCGです。この正規化により、NDCGは0から1のスケールで表現され、スコアが1の場合はアイテムの完璧なランキングを示します。
NDCG is particularly valuable in scenarios where the relevance of results is not binary (relevant or not) but graded, such as in 検索エンジン or recommendation systems. By utilizing NDCG, developers can gain insights into how well their algorithms perform in providing relevant results to users, thereby improving user satisfaction and experience.