For our project, we use k=6.

In this step, we are using StudentEvent dataset. The value for this dataset has been standardized in Rapidminer. It has 35 rows with 11 columns.

import numpy as np

from matplotlib import pyplot as plt

from scipy.cluster.hierarchy import dendrogram

from sklearn.cluster import AgglomerativeClustering

#Alternate to perform scaling using in-built function

from scipy.cluster.hierarchy import dendrogram, linkage

#agglomerative clustering

dag = new_df[['Assignment','Forum','Activity','LectureNote',

'Tutorial','Questionnaire','Quiz','MarksBin']].copy()

dag.info()

X_dag = dag.iloc[:, [0,1,2,3,4,5,6]].values

y_dag = dag.iloc[:, [7]].values

Z=linkage(X_dag,method="ward")

#Plot a Dendogram

fig, ax = plt.subplots(figsize=(10, 10))

ax=dendrogram(Z,orientation="top",labels=np.array(y_dag),leaf_rotation=30,leaf_font_size=10)

plt.tight_layout()

plt.show()

#5 Visualizing the clusters. This code is similar to k-means #visualization code. We only replace the y_kmeans vector name to #y_hc for the hierarchical clustering

plt.scatter(X_dag[y_hc==0, 0], X_dag[y_hc==0, 1], s=100, c='red', label ='Cluster 1')

plt.scatter(X_dag[y_hc==1, 0], X_dag[y_hc==1, 1], s=100, c='blue', label ='Cluster 2')

plt.scatter(X_dag[y_hc==2, 0], X_dag[y_hc==2, 1], s=100, c='green', label ='Cluster 3')

plt.scatter(X_dag[y_hc==3, 0], X_dag[y_hc==3, 1], s=100, c='cyan', label ='Cluster 4')

plt.scatter(X_dag[y_hc==4, 0], X_dag[y_hc==4, 1], s=100, c='magenta', label ='Cluster 5')

plt.scatter(X_dag[y_hc==5, 0], X_dag[y_hc==5, 1], s=100, c='black', label ='Cluster 6')

plt.title('Clusters of Online Learning Participation')

plt.legend()

plt.show()

Based on the reference below, it's up to us where we would like to create the threshold. Therefore, I decided to create 6 clusters based on the line drawn. Therefore the cluster for Agglomerative Clustering in Python is 6.