# Cluster Analysis

### Spatial Interpolation

__Types of Interpolation__

- Global Methods – takes into condideration all known points to estimate the values at unknown locations
- Local Methods – use only a limited set of points from the surrounding area to estimate the value for an unknown point

### Determining Bandwith Size for Kernel Density Analysis in GIS

Determining the search radius for kernel density analysis is highly subjective and GIS users are not always clear on how to go about setting this radius. In my work with this technique, I have come across several ideas on how to set the search radius.

First, some researchers suggest that you should familiarize yourself *a priori* with the study area, run several kernel densities, then make a bandwidth choice based on the bandwith that yields a surface that is more in accordance with one’s prior (subjective) ideas of clustering in the study area. Obviously, for this method to be effective, you have to get into your subject matter and get a feel for the spatial variations of whatever is being modeled.

A second idea is to create a fishnet and overlay the fishnet on the data points. Next, do a spatial join to get a count of the number of points per grid. This is followed by repeated global Moran’s I tests using different distance bands. This can be accomplished easily in ArcGIS. For each distance band, we note the Z-value at which clustering is statistically significant, and these Z-values are graphed against the distance bands. Distance is placed on the x-axis and z-scores on the y-axis. The first peak in the Z-scores represents a reasonable distance band for the search radius.

None of these methods remove the subjectivity from kernel density analysis, but they help to justify whatever bandwidth is selected.