Serendipity

It is related to lucky findings or satisfying surprises. There are two kinds of metrics for serendipity:

1. Primitive recommender based: a first metric is given by: $ser(R_u) = \sum_{k=1}^{|R_u|}max(R_u[k] - PM_u[k],0)rel(i_k)\dfrac{count_k(k)}{k}$, where PM is the primitive recommender and rel is a function that calculates if the predicted items are relevant to the user or not. This other metric uses $UNEXP_u = R_u - PM_u$, which represents the surprising items for the user u, but not the ranking of the items : $ser(R_u) = \dfrac{\sum_{i \in UNEXP_u}utility(i)}{|R_u|}$. A third metric is: $ser(R_u)= \dfrac{(R_u - E_u) \cap USEFUL_u}{|R_u|}$ where USEFUL is the set of useful items and E is the set of expected items.
2. Non primitive recommender based: one metric used is the following: $ser(R_u)= \dfrac{1}{|H_u|} \sum_{i \in H_u} \sum{j \in R_u} \dfrac{cossim(i,j)}{|R_u|}$, where we are considering the cosine similarity between the recommended items and the history of consumption of the user (H). This metric does not consider the usefulness of the recommendations.

The first group of metrics is really sensitive to the choice of the primitive recommender -> the second group could be useful if associated with metrics that consider usefulness of recommended items.

Tags

#recsys