Hierarchical Clustering Lab

Agglomerative clustering merges the two closest patient groups at each step — bottom-up — building a dendrogram without choosing K upfront.

Agglomerative Algorithm

Start: each patient = own cluster Repeat until one cluster remains: 1. Compute pairwise inter-cluster dist 2. Merge two closest clusters 3. Update distance matrix Linkage: Single → min pairwise dist Complete → max pairwise dist Average → mean pairwise dist

Reading the Dendrogram

Height of each merge = distance between merged clusters. Cut the dendrogram horizontally to get a flat clustering — the cut height determines the number of clusters.

High cut → fewer, bigger clusters Low cut → many, smaller clusters Optimal → cut below the longest vertical branch (biggest height gap)

⚖️ Ethical Reality

Hierarchical clustering pipelines in genomics research often use complete linkage, which is sensitive to outliers. A single patient with an anomalous biomarker profile can distort entire cluster merges — causing misclassification of otherwise similar patients.

① Clustering Parameters

Patients (N)16

smaller N = clearer dendrogram

Cut Height threshold3.5

horizontal cut = number of clusters

Linkage Method

② Linkage Formula

        Complete: d(A,B)=max‖a−b‖

        Single:   d(A,B)=min‖a−b‖

        Average:  d(A,B)=mean‖a−b‖

        Merges: 0 of —

x-axis: Patient ID
y-axis: Merge distance (linkage height)
── = cut height threshold

③ Cluster Summary

Clusters at Cut Height

—

Total Merges

—

Max Distance

—

Linkage Used

—

N Patients

④ Dendrogram — each U-shape = one merge event · height = distance · dashed red line = cut threshold · colour = resulting cluster