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NAME

v.nnstat - Indicates clusters, separations or random distribution of point set in 2D or 3D space.

KEYWORDS

vector, nearest neighbour analysis

SYNOPSIS

v.nnstat --help

DESCRIPTION

v.nnstat indicates clusters, separations or random distribution of point dataset in 2D or 3D space using Nearest Neighbour Analysis (NNA). The method is based on comparison of observed average distance between the nearest neighbours and the distance which would be expected if points in the dataset are distributed randomly. More detailed information about theoretical background is provided in (Clark and Evans, 1954), (Chandrasekhar, 1943, p. 86-87). Details about the module and testing are summarized in (Stopkova, 2013).

EXAMPLES

Comparison of 2D and 3D NNA

On the example of dataset that contains 2000 randomly distributed points, basic settings of analysis dimension (2D or 3D) will be examined:

• 2D NNA may be performed using 2D vector layer. If 2D NNA is required to be performed using 3D vector layer, flag -2 should be marked. The results of both cases can be seen below.

  v.nnstat input=rand_2000_2d
  

  Output in the command line:

  Input coordinates have been read... Computing average distance between nearest neighbors... 100% *** Nearest Neighbour Analysis results *** Input settings .. 3D layer: 0 3D NNA: 0 Number of points .......... 2000 Area ...................... 398645718.651701 [units^2] Density of points ......... 0.000005 Average distance between the nearest neighbours ........... 225.859 [units] Average expected distance between the nearest neighbours .. 223.228 [units] Ratio rA/rE ............... 1.011785 *** Results of two-tailed test of the mean *** Null hypothesis: Point set is randomly distributed within the region. Standard variate of the normal curve> c = 1.008239 Null hypothesis IS NOT REJECTED at the significance level alpha = 0.05

  v.nnstat input=rand_2000_3d -2
  

  Output in the command line:

  Input coordinates have been read... Computing average distance between nearest neighbors... 100% *** Nearest Neighbour Analysis results *** Input settings .. 3D layer: 1 3D NNA: 0 Number of points .......... 2000 Area ...................... 398645718.651701 [units^2] Density of points ......... 0.000005 Average distance between the nearest neighbours ........... 225.859 [units] Average expected distance between the nearest neighbours .. 223.228 [units] Ratio rA/rE ............... 1.011785 *** Results of two-tailed test of the mean *** Null hypothesis: Point set is randomly distributed within the region. Standard variate of the normal curve> c = 1.008239 Null hypothesis IS NOT REJECTED at the significance level alpha = 0.05

  NOTE: Comparing the results of 2D NNA with results summarized in (Stopkova, 2013), there can be seen small difference between the values of area. It is assumed to be caused by differences in transformed coordinates of the convex hull that have been computed using two versions of the module.

• 3D NNA can be performed just using 3D vector layer. If 3D NNA is required to be performed using 2D vector layer, name of the column in attribute table that contains elevation values must be set. The results of both cases can be seen below.

  v.nnstat input=rand_2000_3d
  

  Output in the command line:

  Input coordinates have been read... Computing average distance between nearest neighbors... 100% Reading 3D vertices... 100% Constructing 3D hull... 99% *** Nearest Neighbour Analysis results *** Input settings .. 3D layer: 1 3D NNA: 1 Number of points .......... 2000 Volume .................... 398423031180.489197 [units^3] Density of points ......... 0.000000 Average distance between the nearest neighbours ........... 346.072 [units] Average expected distance between the nearest neighbours .. 323.531 [units] Ratio rA/rE ............... 1.069670 *** Results of two-tailed test of the mean *** Null hypothesis: Point set is randomly distributed within the region. Standard variate of the normal curve> c = 0.191691 Null hypothesis IS NOT REJECTED at the significance level alpha = 0.05

  v.nnstat input=rand_2000_2d zcolumn=z
  

  Output in the command line:

  Reading elevations from attribute table: 2000 records selected Input coordinates have been read... Computing average distance between nearest neighbors... 100% Reading 3D vertices... 100% Constructing 3D hull... 99% *** Nearest Neighbour Analysis results *** Input settings .. 3D layer: 0 .. 3D NNA: 1 .. zcolumn: z Number of points .......... 2000 Volume .................... 398423031180.489197 [units^3] Density of points ......... 0.000000 Average distance between the nearest neighbours ........... 346.072 [units] Average expected distance between the nearest neighbours .. 323.531 [units] Ratio rA/rE ............... 1.069670 *** Results of two-tailed test of the mean *** Null hypothesis: Point set is randomly distributed within the region. Standard variate of the normal curve> c = 0.191691 Null hypothesis IS NOT REJECTED at the significance level alpha = 0.05

• Warning: If flag -2 is set up together with zcolumn, the flag will have higher priority and 2D NNA will be performed.

Comparison of various datasets

In (Stopkova, 2013), there might be seen other examples (also clustered and dispersed datasets).

TODO

• add graphical output

SEE ALSO

v.hull

REQUIREMENTS

• LAPACK / BLAS (libraries for numerical computing) for GMATH library (GRASS Numerical Library)
  http://www.netlib.org/lapack (usually available on Linux distros)

AUTHOR

Eva Stopkova
functions for computation of Minimum Bounding Box volume (Minimum Bounding Rectangle area) are based on functions for computing convex hull from the module v.hull (Aime, A., Neteler, M., Ducke, B., Landa, M.)

SOURCE CODE

Available at: v.nnstat source code (history)

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