Collaborative Filtering

Synonyms

Social filtering

Definition

Collaborative filtering assumes a set of n users $\mathcal {U}=\{u_1,\ldots ,u_n\}$ and a set of m items $\mathcal {I}=\{i_1,\ldots ,i_m\}$. Each user u_j expresses opinions about a set of items $\mathcal {I}_{u_j} \subseteq \mathcal {I}$. Many applications assume opinions are expressed through an explicit numeric rating (e.g., one through five stars), but other methods are possible (e.g., hyperlink clicks, Facebook “likes”). For an active user u_a, collaborative filtering predicts the rating $\mathcal {F}$(u_a,i_r) that u_a would give to item i_r such that i_r ∈ $\mathcal {I}_r$ and $\mathcal {I}_{u_a}\cap \mathcal {I}_r=\emptyset$, i.e., the user has not rated the suggested items.

Historical Background

In the early 1990s, collaborative filtering has emerged as one of the many ways to recommend useful information that are relevant to users. Collaborative filters predict how much a user would like a specific item based upon other users who...