1. 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

2. Point Density in ArcMap
Distance=0.3
Distance=3

3. Point Density in ArcMap
Distance=10

4. Kernel Smoothing
Kernel Smoothing is interpolation

5. 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
Density analysis takes known quantities of some phenomena and spreads it across the landscape based on the quantity that is measured at each location and the spatial relationship of the locations of the measured quantities.Why map density? Density surfaces are good for showing where point or line features are concentrated. For example, you might have a point value for each town representing the total number of people in the town, but you want to learn more about the spread of population over the region. Since all the people in each town do not live at the population point, by calculating density you can create a surface showing the predicted distribution of the population throughout the landscape. F(x) = 1/nh2 S K x-X/n
A density function in GIS calculates a magnitude per unit area from point features that fall within a neighborhood around each cell.
Conceptually, a neighborhood is defined around each raster cell center, and the number of points that fall within the neighborhood is totaled and divided by the area of the neighborhood.If a population field setting other than NONE is used, the item's value determines the number of times to count the point. For example, an item with a value of 3 would cause the point to be counted as three points. The values can be integer or floating point. If an area unit is selected, the calculated density for the cell is multiplied by the appropriate factor before it is written to the output raster. For example, if the input ground units are meters, comparing a unit scale factor of meters to kilometers will result in the values being different by a multiplier of 1,000,000 (1000 x 1000).Possible uses include finding density of houses, wildlife observations, or crime reports. The population field can be used to weigh some points more heavily than others, depending on their meaning, or to allow one point to represent several observations. For example, one address might represent a condominium with 6 units, or some crimes might be weighed more severely than others in determining overall crime levels.Increasing the radius will not greatly change the calculated density values. Although more points will fall inside the larger neighborhood, this number will be divided by a larger area when calculating density. The main effect of a larger radius is that density is calculated considering a larger number of points, which can be farther from the raster cell. This results in a more generalized output raster.
How to calculate density in ArcGIS 9.1with Spatial Analyst:
1 Click the Spatial Analyst dropdown arrow and click Density.
2 Click the Input data dropdown arrow and click the input layer.
3 Click the Population field dropdown arrow and click the field you want to use.
4 Click either Kernel or Simple Density type.
5 In the Search radius text box, type a value to determine the distance to search for points or lines from each cell in the output raster.
6 Click the Area units dropdown arrow and choose the units in which the density values should be presented.
7 Specify an output cell size.
8 Type a name for the result, or leave the default to create a temporary result.
9 Click OK.
More info at

6. Width of Kernel Determines smoothness of surface
narrow kernels produce bumpy surfaces
wide kernels produce smooth surfaces

7. 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).
Kernel estimators are based on probability “kernels”, which are regions around each point location
containing some likelihood of animal presence.
The width of the kernel is based on the smoothing parameter (h), which can be determined in a number of
different ways.
The main automated methods for smoothing parameter selection are reference (which is based on
assumptions of bivariate normality) and least-squares cross validation (which is based on properties of the
data).
Kernel methods are either adaptive (where the kernel width increases as the distance between kernels
increases) or fixed (always the same kernel width). Adaptive kernels tend to perform poorly, often
over-estimating home range areas (Powell 2000; Kernohan et al. 2001).
Kernel estimators have a number of features that make them useful for home ranges: they work well with
small amounts of data (approximately 50 locations), they are robust to autocorrelation, they are
nonparametric, they allow multiple centers of activity, and they result in a utilization distribution (UD) rather
than a simple home range outline (Kernohan et al. 2001). A UD is a grid where the value for each cell
represents the probability of the animal occurring in that cell. Among other uses, a UD allows for a more
precise estimate of home range overlap than a simple outline.

8. 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 estimators are based on probability “kernels”, which are regions around each point location
containing some likelihood of animal presence.
The width of the kernel is based on the smoothing parameter (h), which can be determined in a number of
different ways.
The main automated methods for smoothing parameter selection are reference (which is based on
assumptions of bivariate normality) and least-squares cross validation (which is based on properties of the
data).
Kernel methods are either adaptive (where the kernel width increases as the distance between kernels
increases) or fixed (always the same kernel width). Adaptive kernels tend to perform poorly, often
over-estimating home range areas (Powell 2000; Kernohan et al. 2001).
Kernel estimators have a number of features that make them useful for home ranges: they work well with
small amounts of data (approximately 50 locations), they are robust to autocorrelation, they are
nonparametric, they allow multiple centers of activity, and they result in a utilization distribution (UD) rather
than a simple home range outline (Kernohan et al. 2001). A UD is a grid where the value for each cell
represents the probability of the animal occurring in that cell. Among other uses, a UD allows for a more
precise estimate of home range overlap than a simple outline.

9. Kernel Density in ArcGIS

10. Kernel Density
Cell Size = 0.05
Search Radius = 0.4?

11. Kernel Density
Cell Size = 0.05
Search Radius = 10

12. How to select parameters?
What should the cell size be?
What should the search radius be?

13. Origins of Computer Viruses

14. Origins of Spam

15. Kernel Density Analysis
Amelia O’Connor

16. Kernel Density Output

17. Other tool extensions for kernel density:
Home Range Tools
Animal Movement
Biotas
Home Ranger 1.5
KernelHR

18. Spatial Stats Toolbox New in ArcGIS 10 Additional tools in ArcGIS 10.2
By Lauren Rosenshein

19. 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?

20. 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

21. Hot-Spot Analysis Tool

22. 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:
Mitchell, Brian R. (2007) Comparison of Programs for Fixed Kernel Home Range Analysis
Silverman, B. W. Density Estimation for Statistics and Data Analysis. New York: Chapman and Hall, 1986.
ArcGIS 10 resource center; Kernel Density (Spatial Analyst)

23. Extra Slides

24. Density Estimation
Simple point density: Golf courses
Fail
Rockware