Nearest Neighbor Query

Synonyms

NN query; kNN query

Definition

Given a dataset P and a query point q, a k nearest neighbor (kNN) query returns the k closest data points p ₁ ,p ₂ ,...,p _k to q. For any point p∈P−{p ₁ ,p ₂ ,...,p _k }: dist(p _i , q)≤dist(p, q) ∀ 1≤i≤k, where dist depends on the underlying distance metric. The usual metric is the L _x norm, or formally, given two points q, p whose coordinates on the i-th dimension (1≤i≤m) are q _i and p _i respectively, their L _x distance is:

$${{L_x (p,\,q) = (\Sigma _{i = 1 \sim m} \,\left| {p_i - q_i } \right|^x )^{1/x} ,\,{{\rm for}\, x}} \ne \infty, }$$

$$L_x (p,\,q) = \max \ _{i = 1 \sim m} (\left| {p_i - q_i } \right|){{, {\rm for} \,x = }}\infty. $$

Most work on spatial and spatio-temporal databases focuses on Euclidean distance (i.e., L ₂ ), but alternative definitions have been used in various domains (e.g., road networks, time series).

Key Points

Nearest neighbor search constitutes an important component for several tasks such as clustering, outlier...