Cluster quality internal validity after PCA

Question

Last week I asked: Compare clusters quality (internal validity) after and before dimensionality reduction by PCA

I've been trying to calculate internal validity for clusters after PCA using the iris example, but I couldn't.

So far I have this:

data(iris)
library(factoextra)
iris.scaled <- scale(iris[, -5])
# k-means group number of each observation
km.res <- eclust(iris.scaled, "kmeans", k = 3, nstart = 2, graph = FALSE)
km.res$cluster
# Visualize k-means clusters
fviz_cluster(km.res, geom = "point", frame.type = "norm")

# Compute pairwise-distance matrix
dd <- dist(iris.scaled, method ="euclidean")
# Statistics for k-means clustering
km_stats <- cluster.stats(dd,  km.res$cluster)
km_stats 

And I get the following result:

$clus.avg.silwidths
        1         2         3 
0.6363162 0.3473922 0.3933772 

$avg.silwidth
[1] 0.4599482

In order to try to use cluster.stats after PCA I run this:

library(FactoMineR)
library(factoextra)
library(fpc)

iris.pca <- PCA(iris.scaled, graph = FALSE)
iris.hc <- HCPC(iris.pca)

#Here are the individuals and the dimensions
iris.pca$ind$contrib

#here are the clusters
iris.hc$data.clust[,5]

dis <- dist(iris.pca$ind$contrib, method ="euclidean")

#I need clusters to be numeric
p<- as.numeric(iris.hc$data.clust[,5])

km_stats <- cluster.stats(dis, p)
km_stats

But I get this result:

$clus.avg.silwidths
          1           2           3 
 0.39043588 -0.01734689 -0.15697508 

$avg.silwidth
[1] 0.07483054

Answer 1

You didn't run k-means on the output of PCA.

PCA substantially changes the weights of features. It distorts the data heavily. Also, $ind$contrib sounds wrong to me. You don't want to project to contributions.

Hence, a result computed on the original data, but evaluated after PCA is expected to score quite badly.

Answer 2

I think this one works:

distanc <- dist(iris.pca$ind$coord[,1:2], method="euclidean" ) #distances of the first two components
iris.hc$data.clust[,5]  #here are the clusters
clusters<- as.numeric(iris.hc$data.clust[,5])
km_stats <- cluster.stats(distanc, clusters)
km_stats

Now I have:

$clus.avg.silwidths
        1         2         3 
0.6540650 0.4418605 0.4309233 

$avg.silwidth
[1] 0.509168

I'm using the coords of the individuals, is this ok?