## NAME

v.kernel - Generates a raster density map from vector points map.
Density is computed using a moving kernel. Optionally generates a vector density map on a vector network.

## KEYWORDS

vector, kernel density, point density, heatmap, hotspot

## SYNOPSIS

v.kernel
v.kernel --help
v.kernel [-oqnm] input=name [net=name] [output=name] [net_output=name] radius=float [dsize=float] [segmax=float] [distmax=float] [multiplier=float] [node=string] [kernel=string] [--overwrite] [--help] [--verbose] [--quiet] [--ui]

### Flags:

-o
  Try to calculate an optimal radius with given 'radius' taken as maximum (experimental)
-q
  Only calculate optimal radius and exit (no map is written)
-n
  In network mode, normalize values by sum of density multiplied by length of each segment. Integral over the output map then gives 1.0 * mult
-m
  In network mode, multiply the result by number of input points
--overwrite
  Allow output files to overwrite existing files
--help
  Print usage summary
--verbose
  Verbose module output
--quiet
  Quiet module output
--ui
  Force launching GUI dialog

### Parameters:

input=name [required]
  Name of input vector map with training points
net=name
  Name of input network vector map
output=name
  Name for output raster map
net_output=name
  Name for output vector density map
  Outputs vector map if network map is given
radius=float [required]
  Kernel radius in map units
dsize=float
  Discretization error in map units
  Default: 0.
segmax=float
  Maximum length of segment on network
  Default: 100.
distmax=float
  Maximum distance from point to network
  Default: 100.
multiplier=float
  Multiply the density result by this number
  Default: 1.
node=string
  Node method
  Options: none, split
  Default: none
  none: No method applied at nodes with more than 2 arcs
  split: Equal split (Okabe 2009) applied at nodes
kernel=string
  Kernel function
  Options: uniform, triangular, epanechnikov, quartic, triweight, gaussian, cosine
  Default: gaussian

## DESCRIPTION

v.kernel generates a raster density map from vector points data using a moving kernel. Available kernel density functions are uniform, triangular, epanechnikov, quartic, triweight, gaussian, cosine, default is gaussian.

The module can also generate a vector density map on a vector network. Conventional kernel functions produce biased estimates by overestimating the densities around network nodes, whereas the equal split method of Okabe et al. (2009) produces unbiased density estimates. The equal split method uses the kernel function selected with the kernel option and can be enabled with node=split.

## NOTES

The multiplier option is needed to overcome the limitation that the resulting density in case of a vector map output is stored as category (integer). The density result stored as category may be multiplied by this number.

For the gaussian kernel, standard deviation for the gaussian function is set to 1/4 of the radius.

With the -o flag (experimental) the command tries to calculate an optimal radius. The value of radius is taken as maximum value. The radius is calculated based on the gaussian function, using ALL points, not just those in the current region.

## EXAMPLES

Compute density of points (using vector map of schools from North Carolina sample dataset):

    g.region region=wake_30m
    v.kernel input=schools_wake output=schools_density radius=5000 multiplier=1000000
    r.colors map=schools_density color=bcyr

School density

## KNOWN ISSUES

The module only considers the presence of points, but not (yet) any attribute values.

## REFERENCES

- Okabe, A., Satoh, T., Sugihara, K. (2009). A kernel density estimation method for networks, its computational method and a GIS-based tool. International Journal of Geographical Information Science, Vol 23(1), pp. 7-32.
  DOI: 10.1080/13658810802475491

## SEE ALSO

v.surf.rst

Overview: Interpolation and Resampling in GRASS GIS

## AUTHORS

Stefano Menegon, ITC-irst, Trento, Italy
Radim Blazek (additional kernel density functions and network part)

Last changed: $Date$

## SOURCE CODE

Available at: v.kernel source code (history)

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