R language uses the optimal cluster number k-medoids clustering for customer segmentation

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A brief introduction to k-medoids clustering

K-medoids is another clustering algorithm that can be used to find groups in a dataset. K-medoids clustering is very similar to k-means clustering, except for some differences. The optimization function of k-Medoids clustering algorithm is slightly different from that of K-means. In this section, we will study k-medoids clustering.

K – Medoids clustering algorithm

There are many different types of algorithms that can perform k-medoids clustering, of which the simplest and most efficient algorithm is PAM. In PAM, we perform the following steps to find the cluster center:

1. K data points were selected from the scatter graph as the starting point of the clustering center.
2. Calculate their distances from all the points in the scatter plot.
3. Classify each point into the cluster closest to the center.
4. Select a new point in each cluster to minimize the sum of the distances between all points in the cluster and itself.
5. repeatStep 2,Until the center stops changing.

As you can see, the PAM algorithm is the same as the K-means clustering algorithm except for Step 1 and Step 4. For most practical purposes, k-medoids clustering gives almost the same results as K-means clustering. But in some special cases, we have outliers in the data set, so k-medoids clustering is preferred because it is more robust than outliers.

K-medoids clustering code

Realize k-medoID clustering

In this exercise, we will perform k-medoids using R’s pre-built library:

1. Store the first two columns of the dataset in the iris_data variable:

    

   iris_data<-iris[,1:2]
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2. Installation package:

    

   install.packages("cluster")
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3. Importing software packages:

    

   library("cluster")
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4. Store PAM clustering results in the km.res variable:

    

   km<-pam(iris_data,3)
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5. Import libraries:

    

   library("factoextra")
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6. Plot PAM clustering results in the figure:

    

   fviz_cluster(km, data = iris_data,palette = "jco",ggtheme = theme_minimal())
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   The output is as follows:

   Figure: Results of k-medoids clustering

The results of the K-Medoids clustering are not much different from the results of the K-means clustering we did in the previous section.

Thus, we can see that the previous PAM algorithm divides our data set into three clusters that are similar to the clusters we obtained through k-means clustering.

Figure: Results of K-Medoids clustering and K-means clustering

In the previous figure, observe how the centers of the K-means cluster and the K-means cluster are so close, but the centers of the K-means cluster overlap directly with existing points in the data, whereas the centers of the K-means cluster do not.

K-means clustering and K-medoids clustering

K-medoids clustering is used for customer segmentation

K-means and K-medoids clustering is performed using the customer data set and the results are then compared.

Steps:

1. Select just two columns, grocery store and freezer store, to easily visualize the cluster in two dimensions.
2. Draw a diagram using k-Medoids clustering to show four clusters of this data.
3. K-means clustering was used to draw a four-cluster graph.
4. Compare the two graphs to comment on how the results differ between the two methods.

The result will be a K-mean graph of the cluster, as shown below:

Figure: The expected K-means of the cluster

Determine the optimal number of clusters

Types of clustering indicators

There is more than one method to determine the optimal number of clusters in unsupervised learning. Here’s what we’ll look at in this chapter:

• Contour points
• Elbow method/WSS
• The gap between statistics

Contour points

Calculate contour fraction

We learned how to calculate the contour score of a dataset with a fixed number of clusters:

1. Place the first two columns of the IRIS data set (spacer length and spacer width) in the irIS_data variable:

    

2. Implementing k-means clustering:

    

3. Store k-means clusters in km.res variables:

    

4. Store the pair_dis matrix of all data points in the pair_dis variable:

    

5. Calculate the contour score of each point in the data set:

    

6. Draw contour score diagram:

    

   The output is as follows:

7. Figure: The contour score of each point in each cluster is represented by a single bar

The previous figure gives an average contour score of 0.45 for the dataset. It also shows the average contour scores of clusters and point clusters.

We calculate the contour scores of three clusters. However, to determine how many clusters you want to have, you must calculate the profile scores of multiple clusters in the dataset.

Determine the optimal number of clusters

1. Place the first two columns of the dataset (length and width) in the iris_data variable:

2. Import libraries

3. Draw a graph with contour score and number of clusters (maximum 20) :

   Pay attention to

   In the second parameter, you can change k-means to k-medoids or any other type of clustering.

   The output is as follows:

   Figure: Clustering number and average contour fraction

WSS/elbow method

WSS is used to determine the number of clusters

In this exercise, we will see how to use WSS to determine the number of clusters. Perform the following steps.

1. Place the first two columns of the iris data set (septum length and septum width) in the irIS_data variable:

2. Import libraries

3. Chart WSS and cluster number

   The output is as follows:

4. 

   Figure: WSS and cluster number

In the previous figure, we could have chosen the elbow of the figure as k = 3 because after k = 3 the value of WSS starts to fall more slowly. Choosing the elbows of the graph is always a subjective choice, sometimes it is possible to choose k = 4 or k = 2 instead of K = 3, but for this graph, it is clear that k> 5 is the wrong value for K, because they are not the elbows of the graph, but rather where the slope of the graph changes dramatically.

The gap between statistics

The ideal number of clusters is calculated by gap statistics

In this exercise, we will use Gap statistics to calculate the ideal number of clusters:

1. Place the first two columns of the Iris data set (spacer length and spacer width) in the irIS_data variable

    

2. Import factoextra library

    

3. Plot the gap statistics and the number of clusters (up to 20) :

    

   

   Figure 1.35: Gap statistics and cluster numbers

As shown in the figure above, the maximum Gap statistic is k = 3. Therefore, the ideal number of clusters in the dataset is 3.

Find the ideal number of market segments