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I ran kmeans in r with k = 20 centers and 7 scaled variables to cluster with on a data frame with n = 100K.

Using dplyr group_by I was able to view summary data for each of the 20 clusters: the mean of var 1, var 2 etc.

I thought I understood the kmeans algorithm. Start with k centers, apply each observation to the closest centroid, recalculate the mean and repeat till no more movement.

I'm confused about the resulting centroid. I assumed that it was a single number in 7 dimensional space. However when I type (R) mycluster_object$centers I get back a 20 * 7 table with a value for each cluster and variable.

Example:

library(dplyr)
set.seed(123)
myclustering <- kmeans(select(iris, -Species), centers = 3)

 myclustering$centers
  Sepal.Length Sepal.Width Petal.Length Petal.Width
1     5.006000    3.428000     1.462000    0.246000
2     6.850000    3.073684     5.742105    2.071053
3     5.901613    2.748387     4.393548    1.433871

What exactly are these numbers?

Separately, my initial goal was to order the clusters by "closeness". This is why I thought ordering by what I thought centroids to mean would help.

  1. What does myclustering$centers actually show?
  2. Is there a way to order by clusters by how similar or close together they are, accounting for all the variables used?
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The numbers reported for the centers are the coordinates of each center in n-dimensional space. For example, the iris data has 3 centers in 4 D space thus the 3 rows and 4 columns. Your original problem had specified 20 centers(ie rows) and then 7 columns for each dimension.

The kmeans parameter withinss (myclustering$withinss) is the measure of the cluster's sum of the square error, thus a measure of how close each point of the cluster is to the center.

To compute the distance between the centers, the dist() function is helpful.

dist(myclustering$centers)
#          1        2
#2 5.017569         
#3 3.356935 1.797182

thus centers 2 &3 are the closest to each other and centers 1&2 are the farthest apart.

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  • $\begingroup$ Thanks. I'm looking at the distance matrix and wondering if there's a way of ordering the clusters. I can see visually the smallest number for each row, telling me that the corresponding cluster is closest. How could I boil this down to a single vector with which to order by clusters by closeness? $\endgroup$
    – Doug Fir
    Commented Oct 25, 2018 at 19:14
  • $\begingroup$ You can try this where n is the number of centers and d is the result from the dist function: g<-expand.grid(r=1:n, c=1:n); g<-g[g$c<g$r, ]; g$d<-as.vector(d) $\endgroup$
    – Dave2e
    Commented Oct 25, 2018 at 19:34

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