Kernel Density Estimation for Geographic Point Data

Apply kernel density estimation to spatial point observations of volcanoes and visualize the result within an irregular polygonal boundary

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This example estimates the spatial density of volcanic crater locations in western Uganda using kernel density estimation. Since the study region has an irregular, non-convex boundary, the density visualization is restricted to the polygon using a compiled point-in-polygon test.

Load crater locations and the boundary polygon:

In[1]:=

dat=ExampleData[{"Statistics","UgandaVolcanoes"}];poly=ExampleData[{"Statistics","WesternUgandaBorder"}];

Visualize the polygon defining the study region:

In[2]:=

ListLinePlot[poly,PlotStyleThick,FrameTrue,PlotLabel"Non-convex boundary of western Uganda"]

Out[2]=

The boundary is highly irregular and non-convex, which makes simple rectangular plotting ranges inadequate. This visualization motivates the need for an explicit region membership test in the subsequent density plot

Define a test function that determines whether a given point lies inside the boundary. This is later used to restrict the density plot to the valid geographic region. The test is implemented using winding numbers and compiled for efficiency, since it will be evaluated repeatedly during plotting:

In[3]:=

inPolyQ=Compile[{{poly,_Real,2},{x,_Real},{y,_Real}},Block[{Xi,Yi,Xip1,Yip1,u,v,w},{Xi,Yi}=Transpose[poly];Xip1=RotateLeft[Xi];Yip1=RotateLeft[Yi];u=UnitStep[y-Yi];v=RotateLeft[u];w=UnitStep[-((Xip1-Xi)(y-Yi)-(x-Xi)(Yip1-Yi))];Total[(u(1-v)(1-w)-(1-u)vw)]≠0]];

Fit a smooth kernel density model to the point pattern:

In[4]:=

=SmoothKernelDistribution[dat,"SheatherJones"]

Out[4]=

DataDistribution

Type: Multivariate SmoothKernel

Data points: 120



Evaluate the fitted kernel density on a rectangular grid and restrict the visualization to points inside the polygon using RegionFunction:

In[5]:=

dens=ContourPlotPDF[,{x,y}]//Evaluate,{x,0,3000},{y,550,4500},

,RegionFunction(inPolyQ[poly,#1,#2]&),EpilogPoint@dat

Out[5]=

Related Symbols

SmoothKernelDistribution
KernelMixtureDistribution
PDF
ContourPlot
RegionFunction
Compile
ExampleData
ListPlot
ListLinePlot

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Contributed by: Wolfram Staff

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Kernel Density Estimation for Geographic Point Data

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