Normalisierte Discounted Cumulative Gain (NDCG) Metrik
Das Normalisierte Discounted Cumulative Gain (NDCG) metric is widely used in dem Informationsretrieval and Empfehlungssystemen 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 Relevanzscore of the item at rank i.
Als Nächstes normalisiert NDCG den DCG-Wert, indem es ihn durch den idealen DCG (IDCG) teilt, der den DCG der idealen Rangliste darstellt (die bestmögliche Reihenfolge der Elemente basierend auf ihrer Relevanz). Diese Normalisierung ermöglicht es, NDCG auf einer Skala von 0 bis 1 auszudrücken, wobei ein Wert von 1 die perfekte Rangordnung der Elemente anzeigt.
NDCG is particularly valuable in scenarios where the relevance of results is not binary (relevant or not) but graded, such as in Suchmaschinen 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.