Density Estimation

• Converts points to a raster• The density of points in the

neighborhood of a pixel• No “Z” value is used• ArcMap has a simple “Point Density” tool

– Each pixel=number of points within radius• Kernel Density is related to Kernel

Smoothing but different

Density Estimation

• Simple point density: Golf courses

Rockware

Fail

Point Density in ArcMap

Distance=0.3 Distance=3

Point Density in ArcMap

Distance=10

Kernel Smoothing

• Kernel Smoothing is interpolation

Density Estimation Using Kernels

• Creates a raster from points– Weight (attribute) optional– Not really interpolation

• “Kernel function” applied to points near target pixel

• Different functions are available• High parameters make a “wide” pile,

small values make a “narrow” pile

Width of Kernel• Determines

smoothness of surface – narrow kernels

produce bumpy surfaces

– wide kernels produce smooth surfaces

Kernel Density in ArcGIS 10• Under Spatial Analyst -> Kernel

Density• The kernel function is based on the

quadratic kernel function described in Silverman (1986, p. 76, equation 4.5).

Overview• This analysis show where point features are

concentrated.• Estimations are based on probability “kernels”

– regions around each point location containing some likelihood of point presence.

• The width of the kernel is based on the smoothing parameter (h)

• The output is often called a Utilization Distribution (UD) Grid.

• Methods include: minimum convex polygons, bivariate ellipses, adaptive and fixed kernels

Kernel Density in ArcGIS

Kernel Density

• Cell Size = 0.05• Search Radius = 0.4?

Kernel Density

• Cell Size = 0.05• Search Radius = 10

How to select parameters?

• What should the cell size be?• What should the search radius be?

Origins of Computer Viruses

Origins of Email Spam

Kernel Density Analysis

Amelia O’Connor

Kernel Density Output

Other tool extensions for kernel density:

• Home Range Tools• Animal Movement • Biotas• Home Ranger 1.5• KernelHR

Spatial Stats Toolbox

• New in ArcGIS 10• Additional tools in

ArcGIS 10.2• By Lauren

Rosenshein

Hot-Spot Analysis

• Layer may show “hot-spot” but is it really?

• Z-score and P-value are required– Z-score = high or low values together?– P-value = random?

Hot-Spot Analysis

• High z-values indicate a significantly high or low value– 2.5=cluster of high or low

values• P-value is the chance a

pattern is random– 0.01=probably not random

Hot-Spot Analysis Tool

Citations• Bugoni, L., D'Alba, L., and Furness, R. W. (2009) Marine

habitat use of wintering spectacled petrels Procellaria conspicillata, and overlap with longline fishery. Marine Ecology Progress Series 374:273-285.

• Mitchell, Brian R. (2007) Comparison of Programs for Fixed Kernel Home Range Analysis http://www.wildlife.org/wg/gis/newsletter/jun06/hrcompar.htm

• Silverman, B. W. Density Estimation for Statistics and Data Analysis. New York: Chapman and Hall, 1986.

• ArcGIS 10 resource center; Kernel Density (Spatial Analyst) http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//009z0000000s000000.htm– http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#/Un

derstanding_density_analysis/009z0000000w000000/– http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//00

9z00000011000000.htm