k-means method clarification

Question

I am pretty new to k-means and cluster analysis methods, but I am trying to do it on 5 different measures of inequality and redistribution (Gini, P90/P10, Atkinson with different parameters and the percentage of redistribution defined as difference between Gini pre and post social transfers) to check how the 15 countries I have are grouped based on these measures. I am referring to the 4 Welfare regimes defined in literature, so using k=4 as exogenous information and applying the k-means method for clustering.

However, using R in both kmeans command and eclust command from factorextra package the first argument is a matrix and/or a data frame. What is the difference if I use an Euclidean distance matrix as input? For example, what's the mathematical/computational difference between using the following:

hc8<-subset(wave_8, select = c(Gini.Pareto, P90.P10.Pareto, Atkinson.1, Atkinson.2, percent))
hc8 <- scale(hc8)

res.kmean8<-eclust(hc8, "kmeans", k=4, hc_method="ward.D2") 

and using, instead,

res.kmean8<-eclust(dist(hc8)^2, "kmeans", k=4, hc_method="ward.D2")

Thank you for the help and clarification

Answer 1

Kmeans cannot use a distance matrix.

In order to compte means, it needs to have vector data.

If you pass a distance matrix, it will treat the rows as vectors and compute averages of these distances, and squared errors there. This adds hard to understand bias.

The method is just very designed to squared Euclidean.

If you want to use a distance matrix, use PAM (k-medoids) instead. If you want to minimize Euclidean distances, PAM can find better solutions than k-means (but does not necessarily so, because it is constrained to use data points as centers).