Recall at K

Definition

Recall at K (Recall@K) is a metric that help evaluate the performance of recommendation system. It is the proportion of correctly identified relevant items in the top K recommendations out of the total number of relevant items in the dataset.

$Recall@K=\frac{\text{Number of relevant items in K}}{\text{Total number of relevant items}}$

For each user $u$, let $P_u$ be a set of positive items the user will interact, and $R_u$ be a set of items recommended by the model. ${Recall@K}_u=\frac{|P_u\cup R_u|}{|P_u|}$ In top-K recommendation $|R_u|=K$.

Recall@K is not differentiable.