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In the sample code below I would expect a tree with 3 branches if it was really using centroids. Indeed the 2 closest points are A and B with a distance of 1 < sqrt(5)/2. The centroid of cluster (A,B) is (0.5,0) which is also at a distance 1 from C. But this is not what I am observing.

I know that the Lance-Williams formula is used to compute the distances (Centroid linkage clustering with hclust yields wrong dendrogram?). So the distance between (A,B) and C is 0.5*(sqrt(5)/2) + 0.5*(sqrt(5)/2) - 1/4 = 0.868. But what does it mean and what is the link with centroids ?

Sample code : A <- c(0,0) B <- c(1,0) C <- c(0.5, 1) df <- t(data.frame(A=A, B=B, C=C)) plot(df) hc <- hclust(d = dist(df), method = "centroid") library(ggdendro) p <- ggdendrogram(hc, rotate = FALSE, size = 2) p

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