Normalized Discounted Cumulative Gain (NDCG) Metric
The Normalized Discounted Cumulative Gain (NDCG) metric is widely used in information retrieval and recommendation systems 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 relevance score of the item at rank i.
Next, NDCG normalizes the DCG score by dividing it by the Ideal DCG (IDCG), which is the DCG of the ideal ranked list (the best possible ranking of items based on their relevance). This normalization allows NDCG to be expressed on a scale from 0 to 1, where a score of 1 indicates the perfect ranking of items.
NDCG is particularly valuable in scenarios where the relevance of results is not binary (relevant or not) but graded, such as in search engines 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.