generate clustered spatstat marks?

Question

I was wondering if anyone knows how to assign marks in spatstat so that they tend to cluster spatially? I have a set of lat long coordinates that I want to categorize into 4 groups. I have figured out how to randomly assign marks/groups to these points using the following code:

as.ppp(data, window ,marks=factor(sample(1:4,replace=TRUE)))

But I can't figure out how to assign the marks so that groups tend to occupy points closer to one another. As a further complication, I would also like the number of points within each group to be the same, specified number each time. Does anyone have any leads? Thanks in advance!

By the way if your points are lat, long you need to project them to a flat map before distances etc. in spatstat are correctly. See http://stackoverflow.com/questions/35873254/unit-length-in-spatstat for an example of how to project coordinates. — Ege Rubak, Sep 09 '16 at 08:08

score 0 · Answer 1 · answered Sep 08 '16 at 21:06

Typically in spatstat we define models which describe/generate points at random locations and possibly with random marks. If I understand you correctly you have a fixed set of locations and you simply want to assign random marks. How many points do you have? If you don't have too many points a simple suggestion could be to generate a multivariate normally distributed variable and then take the n_1 lowest values for the first mark, the n_2 next values for the second mark, and so on. A simple example with 4 equal sized groups of points:

library(spatstat)
library(mvtnorm)
set.seed(42) # Make reproducible
X <- redwood # Example data
n <- npoints(redwood)
Xdist <- pairdist(X) # n x n matrix of distances in X
decay_rate <- 1 # Parameter for covariance sturcture
sigma <- exp(-decay_rate * Xdist)
m <- rmvnorm(1, rep(0, n), sigma)
breaks <- quantile(m, probs = c(0, .25, .5, .75, 1)) # breaks to cut marks in four equal sized groups
marks(X) <- cut(m, breaks = breaks, include.lowest=TRUE, labels = 1:4)
plot(X)

generate clustered spatstat marks?

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