1 research outputs found
On the Nearest Neighbor of the Nearest Neighbor in Multidimensional Continuous and Quantized Space
The probability that an entity in a set of entities uniformly
distributed in space is the nearest neighbor of its nearest
neighbor is evaluated for generic distances in a multidimensional
environment. Such an expression is then specialized for systems
with norm-based distances and for systems with quantized normbased distance. Examples for scalar products and sup-norm are derived. When applicable, invariances with respect to the underlying distance and entities density are highlighted. Dimensionality effects are investigated