Métrica de Ganancia Cumulativa Descontada Normalizada (NDCG)
El Ganancia Cumulativa Descontada Normalizada (NDCG) metric is widely used in recuperación de información and sistemas de recomendación 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 puntuación de relevancia of the item at rank i.
A continuación, NDCG normaliza la puntuación de DCG dividiéndola por el DCG Ideal (IDCG), que es el DCG de la lista clasificada ideal (la mejor clasificación posible de los ítems basada en su relevancia). Esta normalización permite que NDCG se exprese en una escala de 0 a 1, donde una puntuación de 1 indica la clasificación perfecta de los ítems.
NDCG is particularly valuable in scenarios where the relevance of results is not binary (relevant or not) but graded, such as in motores de búsqueda 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.