How to find highest kernel density point

Question

I've been using spatstat to analyse point patterns in R. Here's an example to put this in context:

library(spatstat)
library(maptools) # to convert sp class to ppp

Some point data:

set.seed(1985)
x <- rnorm(20)
y <- rnorm(20)
p <- SpatialPoints(coords = matrix(c(x, y), ncol = 2))
plot(p)

The challenge is to find the kernel density at each point, not in a continuous field aggregated as cells in a raster image, as calculated by density from spatstat:

p <- as.ppp(p) d <- density.ppp(p, sigma = 0.3) plot(d)

From this one can identify clusters and other useful things, but it does not provide imediate insight into the point that has the highest dot density. So this is a two-part question:

1. How to extract the coordinates of the pixel with the highest density in d?
2. Is there a way to calculate the kernel density only for the 20 points in p?

Answer 1

I'd convert the output to a raster object. Then:

require(spatstat)
require(sp)
require(raster)
set.seed(1985)
x <- runif(20)
y <- runif(20)
p <- SpatialPoints(coords = matrix(c(x, y), ncol = 2))
plot(p)

Then compute densities:

pp = ppp(x,y) # all points in a (0,1) default window
d <- density.ppp(pp, sigma = 0.1)
dp <- density.ppp(pp, sigma = 0.1, at="points")

That's Q2 answered! For Q1 I turn to the raster package:

dr = raster(d)
xyFromCell(dr, which.max(dr))
             x          y
[1,] 0.1523438 0.00390625

Note this is on slightly different data than you because I did it with data on a (0,1) square. Now I've got maptools your max point comes out here:

> dr = raster(d)
> xyFromCell(dr, which.max(dr))
           x         y
[1,] 1.33514 0.3392474