Problem
1

-
Hierarchical Clustering
-
Construct a dendrogram using Ward linkage and Euclidean distance
-
Identify the optimum number of Clusters

Question

Problem 
1
 
-
 ﻿Hierarchical Clustering
-
 ﻿Construct a dendrogram using Ward linkage and Euclidean distance 
-
 ﻿Identify the optimum number of Clusters

Accepted Answer

⚹ To construct a dendrogram using Ward linkage and Euclidean distance for Hierarchical Clustering, follow these steps: ⚹ ‖ ▪ ⋮ Begin with each data point as a separate cluster. ‖ ‖ ▪ ⋮ Calculate the Euclidean distance between all pairs of clusters. ‖ ‖ ▪ ⋮ Use Ward's method to find the pair of clusters that leads to the minimum increase in total within-cluster variance after merging. ‖ ‖ ▪ ⋮ Merge the pair of clusters that results in the minimum increase in total variance. ‖ ‖ ▪ ⋮ Update the distance matrix to reflect the distance between the new cluster and the original clusters. ‖ ‖ ▪ ⋮ Repeat the process until all data points are in a single cluster. ‖ ‖ ▪ ⋮ Draw the dendrogram based on the sequence of merges and the distance at which they occurred. ‖ ⚹ To identify the optimum number of clusters: ⚹ ‖ ▪ ⋮ Examine the dendrogram and look for a large jump in the distance between successive merges, which may indicate the formation of distinct groups. ‖ ‖ ▪ ⋮ Apply the Elbow method, which involves plotting the within-cluster variance against the number of clusters and looking for an "elbow" where the rate of decrease sharply changes. ‖ ‖ ▪ ⋮ Consider using the Silhouette method, which measures how similar an object is to its own cluster compared to other clusters. ‖ ‖ ▪ ⋮ Use the inconsistency coefficient, which compares the height of a link in a cluster hierarchy with the average height of links below it. ‖ ⚹ These methods will help you determine the point at which to cut the dendrogram to obtain the optimal number of clusters.⚹

Sia