CODEWITHSUNDEEP
spatstat
aqeco
aqeco

Reputation: 5

Custom smoothing kernel

I would like to use Smooth.ppp in spatstat to calculate a sort of "moving average" according to a specific function. The specific distance-dependent weights I would like to use are given by a function wt; for simplicity

wt=function(x,y) exp(-1e5*(x-y)^2)

In the extreme case where wt=kernel, I'd expect no smoothing (ie input marks = smoothed estimates). I'm wondering what I am mis-understanding here about the kernel and how it is applied?

remotes::install_github("spatstat/spatstat.core")
n=4; PPP=ppp(rep(1:n,each=n),rep(1:n,n), c(1,n),c(1,n), marks=1:n^2);
smo=Smooth.ppp(PPP,cutoff=2,kernel=wt,at="points")
rbind(marks(PPP),smo)

(I'm using the latest spatstat build to allow estimates at points using a custom kernel)

Upvotes: 0

Views: 168

Answers (1)

Adrian Baddeley
Adrian Baddeley

Reputation: 2963

This example may have been misinterpreted.

The kernel should be a function(x, y) in the R language which gives the value, at a spatial location (x,y), of the kernel centred at the origin (0,0). Generally the kernel takes its largest values when (x,y) is close to (0,0), and drops to zero when (x,y) is far from (0,0).

The function wt defined in your example has values close to 1 along the diagonal line x = y, and drops to zero rapidly away from the diagonal.

That is unusual. It means that a data point at location (a,b) will be 'smoothed' along the infinite line through the data point with unit slope, with equation y = x + b-a, rather than being smoothed over a region close to (a,b) as it normally would.

The example point pattern PPP consists of points along the diagonal y=x.

The smoothed value at a data point is the weighted average of the mark values at all data points, with weights proportional to the kernel value. In your example, the kernel value for each pair of data points, wt(x1-x2, y1-y2), is equal to 1 because all the data and query points lie on the same line with slope 1.

The kernel weights are all equal in this example, so the smoothed values should all be equal to the average mark value, if leaveoneout=FALSE, and if leaveoneout=TRUE then the smoothed value at data point i is the average of the mark values at the data points excluding point i.

Upvotes: 2

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