# k-means method clarification

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")


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


Thank you for the help and clarification