Calculating optimal number of clusters with Nbclust() - r

Question

I would like to calculate the optimal number of clusters for a large dataset: 17 columns and >80.000 rows.
This is my code:
1. Definition of the path
setwd("C:/Users/A/Documents/Master BWL/Masterarbeit")
2. Loading the required packages
library(factoextra); library(cluster); library(skmeans); library(mclust);
library(fpc); library(psda); library(simEd); library (ggpubr);
library(dbscan); library(clustertend); library(MASS); library(devtools);
library(ggbiplot);library(NbClust)
3. Import csv file
WKA_ohneJB <- read.csv("WKA_ohneJB_PCA.csv", header=TRUE, sep = ";", stringsAsFactors = FALSE)
WKA_ohneJB_scaled <- scale(WKA_ohneJB)
# NbClust ()
nb <- NbClust(WKA_ohneJB_scaled , distance = "manhattan", min.nc = 2, max.nc = 7, method = "kmeans")
dput(rbind(head(WKA_ohneJB, 10), tail(WKA_ohneJB, 10)))
structure(list(X = c(1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L,
821039L, 821040L, 821041L, 821042L, 821043L, 821044L, 821045L,
821046L, 821047L, 821048L), BASKETS_NZ = c(1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L),
LOGONS = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), PIS = c(71L, 39L, 50L, 4L,
13L, 4L, 30L, 65L, 13L, 31L, 111L, 33L, 3L, 46L, 11L, 8L,
17L, 68L, 65L, 15L), PIS_AP = c(14L, 2L, 4L, 0L, 0L, 0L,
1L, 0L, 2L, 1L, 13L, 0L, 0L, 2L, 1L, 0L, 3L, 8L, 0L, 1L),
PIS_DV = c(3L, 19L, 4L, 1L, 0L, 0L, 6L, 2L, 2L, 3L, 38L,
8L, 0L, 5L, 2L, 0L, 1L, 0L, 3L, 2L), PIS_PL = c(0L, 5L, 8L,
2L, 0L, 0L, 0L, 24L, 0L, 6L, 32L, 8L, 0L, 0L, 4L, 0L, 0L,
0L, 0L, 0L), PIS_SDV = c(18L, 0L, 11L, 0L, 0L, 0L, 0L, 0L,
0L, 1L, 6L, 0L, 0L, 13L, 0L, 0L, 1L, 15L, 1L, 0L), PIS_SHOPS = c(3L,
24L, 13L, 3L, 0L, 0L, 6L, 28L, 2L, 11L, 71L, 16L, 2L, 5L,
6L, 0L, 1L, 0L, 3L, 2L), PIS_SR = c(19L, 0L, 14L, 0L, 0L,
0L, 2L, 23L, 0L, 3L, 6L, 0L, 0L, 20L, 0L, 0L, 3L, 32L, 1L,
0L), QUANTITY = c(13L, 2L, 18L, 1L, 14L, 1L, 4L, 2L, 5L,
1L, 5L, 2L, 2L, 4L, 1L, 3L, 2L, 8L, 17L, 8L), WKA = c(1L,
1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L,
0L, 0L, 1L, 1L), NEW_CUST = c(0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L), EXIST_CUST = c(1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L), WEB_CUST = c(1L, 0L, 0L, 0L, 1L, 1L, 0L,
1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L), MOBILE_CUST = c(0L,
1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
1L, 0L, 1L, 0L), TABLET_CUST = c(0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 0L),
LOGON_CUST_STEP2 = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L)), row.names = c(1L,
2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 821039L, 821040L, 821041L,
821042L, 821043L, 821044L, 821045L, 821046L, 821047L, 821048L
), class = "data.frame")
Error: Error in na.omit(jeu1) : object 'polygons' not found

Answer 1

Simple means of determining number of clusters is to examine the elbow in the plot of within groups sum of squares and/or average width of the silhouette, the code produces simple plots to examine these...
In order to perform clustering, you need to solve the problem of NaNs after scaling...
WKA_ohneJB_scaled <- as.matrix(scale(data[, c(-1, -2, -18)]))
plot_scree_clusters <- function(x) {
wss <- 0
max_i <- 10 # max clusters
for (i in 1:max_i) {
km.model <- kmeans(x, centers = i, nstart = 20)
wss[i] <- km.model$tot.withinss
}
plot(1:max_i, wss, type = "b",
xlab = "Number of Clusters",
ylab = "Within groups sum of squares")
}
plot_scree_clusters(WKA_ohneJB_scaled)
plot_sil_width <- function(x) {
sw <- 0
max_i <- 10 # max clusters
for (i in 2:max_i) {
km.model <- cluster::pam(x = pc_comp$x, k = i)
sw[i] <- km.model$silinfo$avg.width
}
sw <- sw[-1]
plot(2:max_i, sw, type = "b",
xlab = "Number of Clusters",
ylab = "Average silhouette width")
}
plot_sil_width(WKA_ohneJB_scaled)

Answer 2

Use the Elbow Method, as alluded to by knytt. Here are a couple references that describe the technique.
https://www.r-bloggers.com/finding-optimal-number-of-clusters/
https://uc-r.github.io/kmeans_clustering#elbow
Also, consider using the Affinity Propogation library. The AP library will automatically determine the optimal number of clusters for you. Check out the siple example below.
install.packages("apcluster")
library("apcluster")
c1 <- cbind(rnorm(30,.3,.5),rnorm(30.7,.4))
c2 <- cbind(rnorm(30,.7,.4),rnorm(30.4,.5))
x1 <- rbind(c1,c2)
plot(x1, xlab="", ylab="", pch=19, cex=.8)
apresia <- apcluster(negDistMat(r=2),x1)
s1 <- negDistMat(x1,r=2)
apres1b <- apcluster(s1)
apresia
plot(apresia, x1)
Resource:
https://cran.r-project.org/web/packages/apcluster/vignettes/apcluster.pdf