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I try to find an example to estimate an average value associated to a coordinate, with K nearest neighbors. I found this very help tutorial regional smoothing.

This code can find the k nearest neighbors:

knn50 <- knn2nb(knearneigh(coords, k = 50), row.names = IDs)

Now my question is: how can we calculate simple average values (by averaging the values of the K nearest neighors)?

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    I've added the "r" tag for you.
    – Spacedman
    Sep 29, 2021 at 12:30

1 Answer 1

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Let's make some sample data so people can run it. First a matrix of point coordinates:

> coords = cbind(runif(100), runif(100))

Then suppose we have A measured at each of the 100 points:

> A = runif(100)

And some ID values which we might need:

> IDs = paste0("ID-",1:100)

Then we compute the nearest neighbours (I'm doing 5 nearest for simplicity):

> knn50 <- knn2nb(knearneigh(coords, k = 5), row.names = IDs)

Each element of knn50 is a vector of the index in coords of the neighbours:

> knn50[[1]]
[1] 12 21 55 87 92

So for example we can plot all the points, plot the neighbours of point 5 in green, then point 5 itself in red:

> plot(coords)
> points(coords[knn50[[5]],],col="green",pch=19)
> points(coords[5,,drop=FALSE],col="red",pch=19)

enter image description here

Then if we want to average over some measure at each of those points, here A, we can use sapply and a function that subsets from A according to those nearest elements:

> sapply(1:length(knn50), function(N){mean(A[N])})
  [1] 0.601408386 0.914703926 0.175615202 0.077348561 0.897013793 0.846810226
  [7] 0.252454209 0.878517886 0.364757435 0.973559384 0.691319680 0.330981456
 [13] 0.728837277 0.549587225 0.196916021 0.249273689 0.649543256 0.021006986
 [etc]

giving the mean of A for the 5 nearest neighbours of each of the 100 points. Note the A value of the point itself isn't included.

I'm not sure why you go on to mention the Getis-Ord statistics etc - that seems a bit superfluous to asking how to use the output of a nearest neighbour function like this.

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  • Thank you @Spacedman. For local G stat, I discover this smoothing technique with the mentionned article. And I try to understand how it actually "smooths" the data. I edited my question.
    – John Smith
    Sep 29, 2021 at 15:39
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    You've got two questions there now - the first one about how to use KNN to compute an average, I've answered. You should cut your second question out and make a new post with it.
    – Spacedman
    Sep 29, 2021 at 15:46
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    Thank you Spacedman, I created a new question
    – John Smith
    Sep 29, 2021 at 16:02

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