R – Finding Centroid of Cluster of Points

Question

While searching the web, solutions for finding centroids of polygons come up rather often. What I'm interested in is finding a centroid of a cluster of points. A weighted mean of sorts.

Can you provide some pointers, pseudo code (or even better, an R package that has already solved this) or links of how this issue can be tackled?

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@iant has suggested a method to average coordinates and use that for the centroid. This is exactly what crossed my mind when I saw the right picture on this web page.

Here is some simple R code to draw the following figure that demonstrates this (× is the centroid):

xcor <- rchisq(10, 3, 2)
ycor <- runif(10, min = 1, max = 100)
mx <- mean(xcor)
my <- mean(ycor)

plot(xcor, ycor, pch = 1)
points(mx, my, pch = 3)

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cluster::pam()$medoids returns a medoid of a set of cluster. This is an example from @Joris Meys:

library(cluster)
df <- data.frame(X = rnorm(100, 0), Y = rpois(100, 2))
plot(df$X, df$Y)
points(pam(df, 1)$medoids, pch = 16, col = "red")

Answer 1

just average the X and Y coordinates (multiply by a weight if you want) and there is your centroid.