Predictive Hacks

How to determine the number of Clusters for K-Means in R

We will work with the Breast Cancer Wisconsin dataset, where we will apply the K-Means algorithm to the individual’s features ignoring the dependent variable diagnosis. Notice that all the features are numeric.

# the column names of the dataset
names <- c('id_number', 'diagnosis', 'radius_mean', 
           'texture_mean', 'perimeter_mean', 'area_mean', 
           'smoothness_mean', 'compactness_mean', 
           'symmetry_mean', 'fractal_dimension_mean',
           'radius_se', 'texture_se', 'perimeter_se', 
           'area_se', 'smoothness_se', 'compactness_se', 
           'concavity_se', 'concave_points_se', 
           'symmetry_se', 'fractal_dimension_se', 
           'radius_worst', 'texture_worst', 
           'perimeter_worst', 'area_worst', 
           'smoothness_worst', 'compactness_worst', 
           'concavity_worst', 'concave_points_worst', 
           'symmetry_worst', 'fractal_dimension_worst')
# get the data from the URL and assign the column names
df<-read.csv(url(""), col.names=names)

Scale your Data

Before we apply any cluster analysis, we should scale our data. We will remove the id_number and the diagnosis

scaled_data<>%select(-id_number, -diagnosis)))

Elbow Method

In a previous post, we explained how we can apply the Elbow Method in Python. Here, we will use the map_dbl to run kmeans using the scaled_data for k values ranging from 1 to 10 and extract the total within-cluster sum of squares value from each model. Then we can visualize the relationship using a line plot to create the elbow plot where we are looking for a sharp decline from one k to another followed by a more gradual decrease in slope. The last value of k before the slope of the plot levels off suggests a “good” value of k.

# Use map_dbl to run many models with varying value of k (centers)
tot_withinss <- map_dbl(1:10,  function(k){
  model <- kmeans(x = scaled_data, centers = k)

# Generate a data frame containing both k and tot_withinss
elbow_df <- data.frame(
  k = 1:10,
  tot_withinss = tot_withinss

# Plot the elbow plot
ggplot(elbow_df, aes(x = k, y = tot_withinss)) +
  geom_line() + geom_point()+
  scale_x_continuous(breaks = 1:10)
elbow method

According to the Elbow Method, we can argue that the number of suggested K Clusters are 2.

Silhouette Analysis

Silhouette analysis allows you to calculate how similar each observation is with the cluster it is assigned relative to other clusters. This metric ranges from -1 to 1 for each observation in your data and can be interpreted as follows:

  • Values close to 1 suggest that the observation is well matched to the assigned cluster
  • Values close to 0 suggest that the observation is borderline matched between two clusters
  • Values close to -1 suggest that the observations may be assigned to the wrong cluster

We can determine the number of clusters K using the average silhouette width. We pick the K which maximizes that score.

# Use map_dbl to run many models with varying value of k
sil_width <- map_dbl(2:10,  function(k){
  model <- pam(x = scaled_data, k = k)

# Generate a data frame containing both k and sil_width
sil_df <- data.frame(
  k = 2:10,
  sil_width = sil_width

# Plot the relationship between k and sil_width
ggplot(sil_df, aes(x = k, y = sil_width)) +
  geom_line() + geom_point() +
  scale_x_continuous(breaks = 2:10)

As we can see from the plot above, the “Best” k is 2

Gap Statistic

The gap statistic compares the total intracluster variation for different values of k with their expected values under null reference distribution of the data (i.e. a distribution with no obvious clustering). The reference dataset is generated using Monte Carlo simulations of the sampling process

# compute gap statistic
gap_stat <- clusGap(scaled_data, FUN = kmeans, nstart = 25,
                    K.max = 10, B = 50)


Again, according to the Gap Statistic, the optimum number of clusters is the k=2.

All 3 methods in one package

Let’s see how we can produce the same analysis for the three methods above with a few lines of coding!


# Elbow method
fviz_nbclust(scaled_data, kmeans, method = "wss") +
  geom_vline(xintercept = 2, linetype = 2)+
  labs(subtitle = "Elbow method")

# Silhouette method
fviz_nbclust(scaled_data, kmeans, method = "silhouette")+
  labs(subtitle = "Silhouette method")

# Gap statistic
# nboot = 50 to keep the function speedy. 
# recommended value: nboot= 500 for your analysis.
# Use verbose = FALSE to hide computing progression.
fviz_nbclust(scaled_data, kmeans, nstart = 25,  method = "gap_stat", nboot = 50)+
  labs(subtitle = "Gap statistic method")
elbow method

Visualize the K-Means

Since we determined that the number of clusters should be 2, then we can run the k-means algorithm with k=2. Let’s visualize our data into two dimensions.

fviz_cluster(kmeans(scaled_data, centers = 2), geom = "point", data = scaled_date)

Clusters and Classes in the same plot

Based on the analysis above, the suggested number of clusters in K-means was 2. Bear in mind that in our dataset we have also the dependent variable diagnosis which takes values B and M. Let’s represent at the same plot the Clusters (k=2) and the Classes (B,M).

We will apply PCA by keeping the first two PCs.

# get the PCA of the scaled data
pca_res <- prcomp(scaled_data)

# add the Cluster to the original data frame
df$cluster<-as.factor(kmeans(scaled_date, centers = 2)$cluster)

# add the PC1 and PC2 to the original data frame

# do a scatter plot of PC1, PC2 with a color of cluster on a separate graph 
# for diagnosis is M and B

ggplot(aes(x=PC1, y=PC2, col=cluster), data=df)+geom_point()+facet_grid(.~diagnosis)

As we can see the majority of patients with a “Benign” tumor were in the first cluster and the patients with a “Malignant” tumor at the second cluster.

Share This Post

Share on facebook
Share on linkedin
Share on twitter
Share on email

Leave a Comment

Subscribe To Our Newsletter

Get updates and learn from the best

More To Explore


Image Captioning with HuggingFace

Image captioning with AI is a fascinating application of artificial intelligence (AI) that involves generating textual descriptions for images automatically.


Intro to Chatbots with HuggingFace

In this tutorial, we will show you how to use the Transformers library from HuggingFace to build chatbot pipelines. Let’s