Quote:
Originally Posted by Agemegos
The p.d.f. for nearest neighbour at distance x, for a uniform random distribution (i.e a Poisson process) is given here as 1-e^-(density * volume). For the case of a Poisson process on a 2-D plane that ends up implying that the average nearest-neighbour distance is 0.5/sqrt(number/area). |
Ah! It generalises to n dimensions with the appropriate generalisation of volume and density. The expected distance to the nearest neighbour is the radius of an n-ball with generalised volume equal to π/4λ, where λ is the generalised density (i.e. number of features per unit of generalised volume.