Find the centroid of Clusters generated by the hclust function

Question

I need to get the centroid for each cluster computed by the hierarchical method. First, this is a part of my dataset to get reproductible example:

> dput(DATABASE[1:20,])
structure(list(TYPE_PEAU = c(2L, 2L, 3L, 2L, 2L, 2L, 2L, 4L, 
3L, 2L, 2L, 2L, 2L, 1L, 4L, 2L, 2L, 2L, 4L, 2L), SENSIBILITE = c(3L, 
2L, 3L, 3L, 3L, 1L, 3L, 3L, 3L, 3L, 3L, 3L, 2L, 2L, 3L, 3L, 3L, 
1L, 3L, 3L), IMPERFECTIONS = c(2L, 2L, 3L, 3L, 1L, 2L, 2L, 3L, 
2L, 2L, 2L, 1L, 1L, 1L, 3L, 1L, 2L, 1L, 2L, 2L), BRILLANCE = c(3L, 
3L, 1L, 3L, 1L, 3L, 3L, 1L, 1L, 3L, 3L, 3L, 3L, 2L, 3L, 3L, 3L, 
3L, 3L, 3L), GRAIN_PEAU = c(3L, 3L, 3L, 1L, 3L, 3L, 3L, 2L, 3L, 
2L, 1L, 3L, 1L, 1L, 3L, 1L, 3L, 3L, 1L, 3L), RIDES_VISAGE = c(3L, 
1L, 1L, 3L, 1L, 3L, 3L, 3L, 3L, 3L, 2L, 1L, 3L, 1L, 3L, 3L, 3L, 
3L, 3L, 3L), MAINS = c(2L, 2L, 3L, 3L, 1L, 1L, 1L, 3L, 3L, 3L, 
3L, 3L, 1L, 3L, 3L, 3L, 3L, 3L, 3L, 2L), PEAU_CORPS = c(2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 2L, 2L, 3L, 2L, 3L, 2L, 3L, 2L, 
2L, 1L), INTERET_ALIM_NATURELLE = c(1L, 1L, 3L, 1L, 1L, 1L, 1L, 
1L, 1L, 3L, 1L, 3L, 1L, 3L, 1L, 3L, 1L, 1L, 1L, 1L), INTERET_ORIGINE_GEO = c(1L, 
1L, 2L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 3L, 1L, 1L, 3L, 3L, 1L, 
1L, 1L, 1L), INTERET_VACANCES = c(1L, 2L, 3L, 1L, 1L, 1L, 1L, 
2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 3L, 1L, 2L), INTERET_ENVIRONNEMENT = c(1L, 
3L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L), AGE_INTERVAL = c(3L, 3L, 4L, 2L, 2L, 3L, 3L, 4L, 
4L, 3L, 4L, 2L, 1L, 3L, 3L, 2L, 2L, 2L, 2L, 3L), ATTENTE_BEAUTE_1 = c(1L, 
6L, 4L, 4L, 6L, 6L, 3L, 1L, 1L, 4L, 3L, 6L, 2L, 5L, 5L, 6L, 7L, 
4L, 6L, 3L), ATTENTE_BEAUTE_2 = c(2L, 2L, 3L, 6L, 4L, 1L, 4L, 
7L, 2L, 2L, 2L, 4L, 4L, 4L, 4L, 2L, 6L, 2L, 2L, 2L), MILIEU_VIE = c(1L, 
1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L), PROFIL_SELECTIONNE = c(1L, 32L, 21L, 23L, 34L, 31L, 
15L, 6L, 1L, 20L, 14L, 34L, 9L, 28L, 28L, 32L, 42L, 20L, 32L, 
14L), NOMBRE_ACHAT = c(14L, 6L, 3L, 9L, 8L, 13L, 10L, 14L, 4L, 
3L, 10L, 8L, 12L, 3L, 7L, 6L, 4L, 13L, 3L, 3L), NOMBRE_CADEAU = c(2L, 
1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 
2L, 1L, 1L)), .Names = c("TYPE_PEAU", "SENSIBILITE", "IMPERFECTIONS", 
"BRILLANCE", "GRAIN_PEAU", "RIDES_VISAGE", "MAINS", "PEAU_CORPS", 
"INTERET_ALIM_NATURELLE", "INTERET_ORIGINE_GEO", "INTERET_VACANCES", 
"INTERET_ENVIRONNEMENT", "AGE_INTERVAL", "ATTENTE_BEAUTE_1", 
"ATTENTE_BEAUTE_2", "MILIEU_VIE", "PROFIL_SELECTIONNE", "NOMBRE_ACHAT", 
"NOMBRE_CADEAU"), row.names = c(NA, 20L), class = "data.frame")

then I used as follow :

mydist = dist(DATABASE)
clusters = cutree(hclust(mydist),k=3)

> clusters
  [1] 1 2 3 3 2 2 3 1 1 3 1 2 1 3 2 2 2 3 2 1 3 2 1 1 1 1 2 1 2 1 3 3 2 3 2 2 1 1 1 1 3 2 1 1 3 2 1 2 2 1 2 2 3 1 3 1 3
 [58] 1 3 2 2 1 1 2 1 2 2 2 3 2 3 1 2 2 1 1 3 3 2 1 2 2 1 2 3 3 3 1 2 1 2 1 1 1 1 1 3 2 2 2 1 1 3 2 2 1 1 1 2 1 1 1 1 3
[115] 1 2 2 1 2 3 1 1 2 3 1 1 1 2 1 3 1 2 3 2 2 1 2 1 1 3 3 2 1 2 2 1 1 1 1 2 1 2 2 3 3 1 1 3 1 3 3 3 3 2 3 1 2 3 3 3 1
[172] 1 2 2 1 1 2 1 2 2 1 3 3 1 2 2 1 1 1 2 2 1 1 1 1 3 2 3 3 1 1 2 2 2 3 1 1 1 2 2 1 2 1 3 1 2 1 3 3 1 1 1 1 2 1 2 2 2
[229] 3 3 1 1 2 1 3 2 2 2 1 1 2 1 3 1 2 1 3 1 3 1 3 1 1 1 1 2 2 1 3 3 3 2 1 2 3 2 2 1 1 3 1 2 3 1 1 2 1 1 1 1 2 2 2 3 2
[286] 1 2 1 1 2 1 2 1 2 2 1 2 3 1 3 1 3 1 1 3 1 1 2 2 1 3 3 2 2 1 2 1 1 2 2 1 3 3 2 2 1 3 3 3 1 1 1 1 3 3 2 1 3 1 2 1 2
[343] 1 2 3 3 2 3 1 3 2 3 3 1 2 2 1 2 2 3 2 1 3 2 2 1 2 3 2 3 3 3 2 2 3 2 1 1 1 2 3 2 2 1 2 2 2 1 2 1 1 1 3 1 2 2 1 1 2
[400] 1 1 1 1 1 2 2 2

Please Note that the objectif is to compute the inter and intra inertia: So i need to compute the distance between each centroid and all points that are included in its cluster.

So I need to compute the distance between each centroid and its concerned cluster to used then for computing the inter and intra inertia.

Answer 1

You can define the centroids as the means of variables, per cluster, in DATABASE.

mydist <- dist(DATABASE)
clusters <- cutree(hclust(mydist), k = 3)
## Col means in each cluster
apply(DATABASE, 2, function (x) tapply(x, clusters, mean))
## or
DATABASE$cluster <- clusters # add cluster to DATABASE
# Now take means per group
library(dplyr)
centroids <- DATABASE %>%
        group_by(cluster) %>%
        summarise_all(funs(mean))
## Distance between centroids
dist(centroids[, -1], method = "euclidean")
## Example for distance in cluster 1 (distance between all observations of cluster 1)
DATABASE %>%
        filter(cluster == 1) %>%
        select(-cluster) %>%
        dist()

Answer 2

you might want to specify your k value into 1:3 not just 3

here is the code and how to find the center (mean)