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Nearest Neighbour Analysis

  1. Oct 13, 2004 #1
    Does anyone know how the mathematics behind the Nearest Neighbour Analysis/Index work?
    It is used in biology and geography and shows the dispersion of for example plants or shoe-shops.
  2. jcsd
  3. Oct 13, 2004 #2
    i dunno but this sounds vaguely familiar with clustering ...
    are u talking abt clustering ??

    -- AI
  4. Oct 15, 2004 #3
    Yes it is about clustering...
    You have an area, A, in which you have a number of points, n. For every point you measure the distance to its nearest neighbour. Then you calculate the mean nearest neighbour distance, d.
    Then you use the formula NNI=2d*square-root(n/A)
    Values for NNI close to 0 means clustered distribution, around 1 random distribution and close to the maximum value 2,15 uniform distribution.
    I do not understand why 2.15 is the largest value you can get and why a value of 1 indicates a random distribution.
    Anyone that knows? I would bwe thakful if you helped me...
  5. Oct 17, 2004 #4
    I have not done much of NNI .....
    But as i see ur formula for NNI , i thought of doing a bit of reverse engineering .....

    case > clustered points
    If we set n and A as constant, then it may be shown that d = radius of a cluster
    So it gets pretty intuitive, as to why if NNI -> 0 , would mean high clustering since NNI>0 means radii of cluster is reducing thereby increased clustering ...

    Doing a bit more of this,
    we may come to a conclusion that
    NNI for cluster < NNI for random < NNI for uniform

    However the values of 1 and 2.15 don't seem to come up anywhere throughout ....
    So i feel they are statistical limits and not theoretical ones ....
    I may be wrong , but i just thought if i am wrong , it may generate counter arguments ....

    -- AI
  6. Aug 2, 2011 #5
    The upper limit comes from an observation that in the plane hexagonal spacing (each point has six equidistant neighbours) maximizes the distance between neighbours for a given density. You can read about it in this reference:

    "Distance to Nearest Neighbour as a Measure of Spatial Relationships in Populations"

    Clark and Evans, Ecology, Vol 35. No 4, 1954.

    They also refer to earlier work by Hertz in 1909. The appendix gives a derivation of this measure.
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