Determining Clustering using R

Task of Lab

The objective of this lab was to determine if maple trees within a study area in Lansing, Michigan are clustered or not using Kernel Density Estimation (KDE), Ghat, and Fhat functions in R.

Methodology

Code for each step is below:

1. Imported my CSV dataset of maple tree coordinates into R.

2. Found the Mean Center and plotted the Standard Distance as a circle centered at the Mean Center.

3.  Performed a KDE estimation for my maple tree dataset.

4. Found the mean nearest neighbor distance for the maple tree dataset and presented the distribution of nearest neighbor distances as a histogram.

5. Determined Ghat for the maple tree dataset to find evidence of clustering.

6. Determined Fhat for the maple tree dataset to find more evidence of clustering to prove robustness.

R Packages and Functions Used 

Base R Functions:

• bw.nrd0() - chooses the bandwidth of a Gaussian kernel density estimator using  Silverman's "rule-of-thumb" formula

• c() - combines arguments to form a vector

• cbind() - takes a sequence of vector, matrix, or dataframe arguments and combines them by column

• hist() - computes a histogram of the defined values in a vector

• image() - creates a grid of colored or gray-scale rectangles with colors corresponding to the values of the input

• lines() - joins coordinate points with line segments

• max() - returns the maximum value of the input arguments

• mean() - generic function for the arithmetic mean

• min() - returns the minimum value of the input arguments

• plot() - draws a scatter plot with axes and titles in the active graphics window. A line plot can be set by denoting the "type" as "l" (lowercase L)

• read.csv() - reads a csv file and creates a data frame from it

• seq() - generates a sequence of numbers from a defined minimum to a defined maximum by a defined interval

• summary() - provides a statistical summary for the input vector

• symbols() - draws symbols on a plot

sf Package Functions:

• st_as_sf() - converts a foreign object to an sf object

sfdep Package Functions:

• std_distance() - measures the distance away from the mean center of a point pattern

splancs Package Functions:

• areapl() - calculates the area of a polygon

• as.points() - creates data in spatial point format ([x,y] coordinates)

• csr() - generates completely spatially random points on a polygon

• Fhat() - calculates an estimate of the F nearest neighbor distribution function

• Ghat() - calculates an estimate of the G nearest neighbor distribution function

• kernel2d() - performs quartic kernel smoothing on a point pattern

• nndistG() - calculates nearest neighbor distances as used by Ghat

• npts() - returns the number of points in a data set

Code

Step 1 Code: 

> Maple<-read.csv("C:\\Users\\...\\Lab_data\\data\\dataexer\\lansing_maple.csv",header=T)

Results

After completing KDE, Ghat, and Fhat calculation, there is evidence of clustering of maple trees in the studied area of Lansing, Michigan. The biggest clusters of maple trees are located in the central part, the southeast corner, and the southwest corner of the study area.