🔎 NDCG (Normalized Discounted Cumulative Gain)

NDCG (Normalized Discounted Cumulative Gain)#

DCG normalised by the ideal ordering, bounded between 0 and 1.

Important

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What it is#

Normalized Discounted Cumulative Gain measures ranking quality using both graded relevance and position. It sums each item’s relevance with a logarithmic discount for lower ranks (DCG), then divides by the ideal ordering’s score (IDCG):

\[\text{NDCG@}K = \frac{\text{DCG@}K}{\text{IDCG@}K} \in [0, 1].\]

A perfect ranking scores 1.

Why it’s powerful#

Unlike Hit Rate, NDCG rewards putting highly relevant items near the top and handles multi-level relevance (a 5-star match beats a 3-star one). Normalizing by IDCG makes it comparable across users with different numbers of relevant items — the reason it is the default offline ranking metric for recommenders and search.

In recsys#

Computed per user then averaged, NDCG@K captures the personalized-ordering quality that drives engagement. It is the recommender-system application of the same DCG used in information retrieval, so IR and recsys share this yardstick.

Theme: Ranking & Interleaving · All terminology

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Mind map — connected ideas

DCG (Discounted Cumulative Gain) · Mean Average Precision (MAP) · Hit Rate (HR) · Average Precision (AP) · Relevance in Recommender Systems · Intra-List Diversity (ILD)

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More in Ranking & Interleaving

Balanced Interleaving · DCG (Discounted Cumulative Gain) · Interleaving Tests · Mean Average Precision (MAP) · Probabilistic Interleaving · Ranking Algorithms · Team Draft Interleaving (TDI) · TREC (Text REtrieval Conference)