Prerequisites: Agglomerative Clustering Agglomerative Clustering is one of the most common hierarchical clustering techniques. Dataset – Credit Card Dataset. Assumption: The clustering technique assumes that each data point is similar enough to the other data points that the data at the starting can be assumed to be clustered in 1 cluster. Step 1: Importing the required libraries
Python3
import pandas as pdimport numpy as npimport matplotlib.pyplot as pltfrom sklearn.decomposition import PCAfrom sklearn.cluster import AgglomerativeClusteringfrom sklearn.preprocessing import StandardScaler, normalizefrom sklearn.metrics import silhouette_scoreimport scipy.cluster.hierarchy as shc |
Step 2: Loading and Cleaning the data
Python3
# Changing the working location to the location of the filecd C:\Users\Dev\Desktop\Kaggle\Credit_CardX = pd.read_csv('CC_GENERAL.csv')# Dropping the CUST_ID column from the dataX = X.drop('CUST_ID', axis = 1)# Handling the missing valuesX.fillna(method ='ffill', inplace = True) |
Step 3: Preprocessing the data
Python3
# Scaling the data so that all the features become comparablescaler = StandardScaler()X_scaled = scaler.fit_transform(X)# Normalizing the data so that the data approximately# follows a Gaussian distributionX_normalized = normalize(X_scaled)# Converting the numpy array into a pandas DataFrameX_normalized = pd.DataFrame(X_normalized) |
Step 4: Reducing the dimensionality of the Data
Python3
pca = PCA(n_components = 2)X_principal = pca.fit_transform(X_normalized)X_principal = pd.DataFrame(X_principal)X_principal.columns = ['P1', 'P2'] |
Dendrograms are used to divide a given cluster into many different clusters. Step 5: Visualizing the working of the Dendrograms
Python3
plt.figure(figsize =(8, 8))plt.title('Visualising the data')Dendrogram = shc.dendrogram((shc.linkage(X_principal, method ='ward'))) |
To determine the optimal number of clusters by visualizing the data, imagine all the horizontal lines as being completely horizontal and then after calculating the maximum distance between any two horizontal lines, draw a horizontal line in the maximum distance calculated. 
The above image shows that the optimal number of clusters should be 2 for the given data. Step 6: Building and Visualizing the different clustering models for different values of k a) k = 2
Python3
ac2 = AgglomerativeClustering(n_clusters = 2)# Visualizing the clusteringplt.figure(figsize =(6, 6))plt.scatter(X_principal['P1'], X_principal['P2'], c = ac2.fit_predict(X_principal), cmap ='rainbow')plt.show() |
b) k = 3
Python3
ac3 = AgglomerativeClustering(n_clusters = 3)plt.figure(figsize =(6, 6))plt.scatter(X_principal['P1'], X_principal['P2'], c = ac3.fit_predict(X_principal), cmap ='rainbow')plt.show() |
c) k = 4
Python3
ac4 = AgglomerativeClustering(n_clusters = 4)plt.figure(figsize =(6, 6))plt.scatter(X_principal['P1'], X_principal['P2'], c = ac4.fit_predict(X_principal), cmap ='rainbow')plt.show() |
d) k = 5
Python3
ac5 = AgglomerativeClustering(n_clusters = 5)plt.figure(figsize =(6, 6))plt.scatter(X_principal['P1'], X_principal['P2'], c = ac5.fit_predict(X_principal), cmap ='rainbow')plt.show() |
e) k = 6
Python3
ac6 = AgglomerativeClustering(n_clusters = 6)plt.figure(figsize =(6, 6))plt.scatter(X_principal['P1'], X_principal['P2'], c = ac6.fit_predict(X_principal), cmap ='rainbow')plt.show() |
We now determine the optimal number of clusters using a mathematical technique. Here, We will use the Silhouette Scores for the purpose. Step 7: Evaluating the different models and Visualizing the results.
Python3
k = [2, 3, 4, 5, 6]# Appending the silhouette scores of the different models to the listsilhouette_scores = []silhouette_scores.append( silhouette_score(X_principal, ac2.fit_predict(X_principal)))silhouette_scores.append( silhouette_score(X_principal, ac3.fit_predict(X_principal)))silhouette_scores.append( silhouette_score(X_principal, ac4.fit_predict(X_principal)))silhouette_scores.append( silhouette_score(X_principal, ac5.fit_predict(X_principal)))silhouette_scores.append( silhouette_score(X_principal, ac6.fit_predict(X_principal)))# Plotting a bar graph to compare the resultsplt.bar(k, silhouette_scores)plt.xlabel('Number of clusters', fontsize = 20)plt.ylabel('S(i)', fontsize = 20)plt.show() |
Thus, with the help of the silhouette scores, it is concluded that the optimal number of clusters for the given data and clustering technique is 2.
