• 🤷 We might not know in advance the number of distinct clusters ‘k’ in the dataset.
• 🕸️ Also, sometimes the dataset may contain a nested structure or some inherent hierarchy, such as, file system, organizational chart, biological lineages, etc.

⭐️ Method of cluster analysis that seeks to build a hierarchy of clusters, resulting in a tree like structure called dendrogram.

👉Hierarchical clustering allows us to explore different possibilities (of ‘k’) by cutting the dendrogram at various levels.

Agglomerative (Bottom-Up):
Most common, also known as Agglomerative Nesting (AgNes).

1. Every data point starts as its own cluster.
2. In each step, merge the two ‘closest’ clusters.
3. Repeat step 2, until all points are merged in a single cluster.

Divisive (Top-Down):

1. All data points start in one large cluster.
2. In each step, divide the cluster into two halves.
3. Repeat step 2, until every point is its own cluster.

Agglomerative Clustering Example:

• Ward’s Method:
  • Merges clusters to minimize the increase in the total within-cluster variance (sum of squared errors), resulting in compact, equally sized clusters.
• Single Linkage (MIN):
  • Uses the minimum distance between any two points in different clusters.
  • Prone to creating long, ‘chain-like’ 🔗 clusters, sensitive to outliers.
• Complete Linkage (MAX):
  • Uses the maximum distance between any two points in different clusters.
  • Forms tighter, more spherical clusters, less sensitive to outliers than single linkage.
• Average Linkage:
  • Combines clusters by the average distance between all points in two clusters, offering a compromise between single and complete linkage.
  • A good middle ground, often overcoming limitations of single and complete linkage.
• Centroid Method:
  • Merges clusters based on the distance between their centroids (mean points).

👉Single Linkage is more sensitive to outlier than Complete Linkage, as Single Linkage can keep linking to the closest point forming a bridge to outlier.

👉All cluster linkage distances.

👉We get different clustering using different linkages.