Mixing PCA and K-means

Here we will see how to combine the use of PCA and K-means so that interpretation of clustering may be (hopefully) easier.

First, of course, retrieve the data.

url <- "http://mribatet.perso.math.cnrs.fr/CentraleNantes/Data/Ligue1Fifa22.csv"
data <- read.table(url)
dim(data)

[1] 129  52

## Ouch plenty of features

Let’s start with the PCA. Here I treat qualitative variable as we should do and add as supplementary quantitative the overall score (since it is probably a (weighted?) average of other scores).

library(FactoMineR)

Registered S3 method overwritten by 'htmlwidgets':
  method           from         
  print.htmlwidget tools:rstudio

pca <- PCA(data, quali.sup = c(1, 9, 10, 12), quanti.sup = 2, ncp = 10)

## Now I should interpret the PCA as we learnt in the lecture

We can move to unsupervised clustering with the k–means using the PCA coordinates. Here I will keep only the first 10 factorial axis (hence npc = 10 in the call to PCA above). I will use 4 clusters but you know how to select the right number of clusters…

pca_coord <- pca$ind$coord
my_clust <- kmeans(pca_coord, 4, nstart = 100)

Based on this clustering we can do a nice plot mixing individual positions on the first factorial plane and clustering.

player_names <- rownames(data)
plot(pca_coord[,1:2], type = "n")##set the plot without actually plotting points
text(pca_coord[,1:2], labels = player_names, col = my_clust$cluster)

Now, because of the first analysis done in PCA, you can easily interpret the meaning of each clusters.