Reverse Nearest Neighbor Query

Synonyms

Reverse nearest neighbor search; RNN query

Definition

Given a multidimensional dataset P and a point q, a reverse nearest neighbor (RNN) query retrieves all the points p∈P that have q as their nearest neighbor. The set RNN(q) of reverse nearest neighbors of q is called the influence set of q. Formally, RNN(q) = {p∈P | ¬∃p′∈P such that dist(p,p′) < dist(p,q)}, where dist is a distance metric (Euclidean distance is assumed in the following examples).

The definition can also be extended to reverse k nearest neighbors (RkNN). Specifically, a RkNN query retrieves all the points p∈P that have q as one of their k nearest neighbors. In this case, RkNN(q) = {p∈P | dist(p,q) ≤ dist(p,p_k), where p_k is the k-th NN of p}.

Historical Background

Reverse nearest neighbor queries were proposed in [4] and have received considerable attention due to their importance in several applications involving decision support, resource allocation, profile-based marketing, etc. Fig. 1shows an example...