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.
On the Nearest Neighbor of the Nearest Neighbor in Multidimensional Continuous and Quantized Space
ROVATTI, Riccardo;MAZZINI, Gianluca
2008
Abstract
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.File in questo prodotto:
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