How to visualize a distance matrix on the map by the thickness or color of the line connect the adjacent localities in R?

Question

Suppose I have two datasets: (1) a data frame: coordinates of localities, each with ID; and (2) a linguistic distance matrix which reflects the linguistic distance between these localities.

# My data are similar to this structure 
# dataframe
id <- c("A","B","C","D","E")
x_coor <- c(0.5,1,1,1.5,2)
y_coor <- c(5.5,3,7,6.5,5)
my.data <- data.frame(id = id, x_coor = x_coor, y_coor = y_coor)

# linguistic distance matrix
       A          B          C          D
B 308.298557                                 
C 592.555483 284.256926                      
D 141.421356 449.719913   733.976839           
E 591.141269 282.842712   1.414214     732.562625

Now, I want to visualize the linguistic distance between every two sites onto a map by the thickness or color of the line connect the adjacent localities in R.

Just like this: enter image description here

My idea is to generate the delaunay triangulation by deldir or tripack package in R.

# generate delaunay triangulation
library(deldir)
de=deldir(my.data$x_coor,my.data$y_coor)
plot.deldir(de,wlines="triang",col='blue',wpoints = "real",cex = 0.1)
text(my.data$x_coor,my.data$y_coor,my.data$id)

this is the plot: enter image description here

My question is how to reflect the linguistic distance by the thickness or color of the edges of triangles? Is there any other better method?

Thank you very much!

Answer 1

What you want to do in respect of the line widths can be done "fairly easily" by the deldir package. You simply call plot.deldir() with the appropriate value of "lw" (line width).

At the bottom of this answer is a demonstration script "demo.txt" which shows how to do this in the case of your example. In particular this script shows how to obtain the appropriate value of lw from the "linguistic distance matrix". I had to make some adjustments in the way this matrix was presented. I.e. I had to convert it into a proper matrix.

I have rescaled the distances to lie between 0 and 10 to obtain the corresponding values of the line widths. You might wish to rescale in a different manner.

In respect of colours, there are two issues:

(1) It is not at all clear how you would like to map the "linguistic distances" to colours.

(2) Unfortunately the code for plot.deldir() is written in a very kludgy way, whence the "col" argument to segments() cannot be appropriately passed on in the same manner that the "lw" argument can. (I wrote the plot.deldir() code a long while ago, when I knew far less about R programming than I know now! :-))

I will adjust this code and submit a new version of deldir to CRAN fairly soon.

#
# Demo script
#

# Present the linguistic distances in a useable way.
vldm <- c(308.298557,592.555483,284.256926,141.421356,449.719913,
         733.976839,591.141269,282.842712,1.414214,732.562625)
ldm <- matrix(nrow=5,ncol=5)
ldm[row(ldm) > col(ldm)] <- vldm
ldm[row(ldm) <= col(ldm)] <- 0
ldm <- (ldm + t(ldm))/2
rownames(ldm) <- LETTERS[1:5]
colnames(ldm) <- LETTERS[1:5]

# Set up the example data.  It makes life much simpler if
# you denote the "x" and "y" coordinates by "x" and "y"!!!
id <- c("A","B","C","D","E")
x_coor <- c(0.5,1,1,1.5,2)
y_coor <- c(5.5,3,7,6.5,5)
# Eschew nomenclature like "my.data".  Such nomenclature
# is Micro$oft-ese and is an abomination!!!
demoDat <- data.frame(id = id, x = x_coor, y = y_coor)

# Form the triangulation/tessellation.
library(deldir)
dxy <- deldir(demoDat)

# Plot the triangulation with line widths proportional
# to "linguistic distances".  Note that plot.deldir() is
# a *method* for plot, so you do not have to (and shouldn't)
# type the ".deldir" in the plotting command.
plot(dxy,col=0) # This, and plotting with "add=TRUE" below, is
                # a kludge to dodge around spurious warnings.
ind <- as.matrix(dxy$delsgs[,c("ind1","ind2")])
lwv <- ldm[ind]
lwv <- 10*lwv/max(lwv)
plot(dxy,wlines="triang",col='grey',wpoints="none",
            lw=10*lwv/max(lwv),add=TRUE)
with(demoDat,text(x,y,id,col="red",cex=1.5))