Hierarchical clustering (Ward)

When to consider it

• Explore nested groups with Ward clustering on numeric Euclidean distances.

Assumptions and scope

• Choose meaningful numeric features and scaling. Do not use arbitrary nominal category codes as distances.

Partial coverage of CTTIR’s mixed/small-sample branch: numeric Ward only; no mixed-type distances.

Required inputs

• Observations × numeric features — Numeric observations; preserve the row and column structure described above.
• Number of clusters — Enter the method parameter described above.
• Standardize features — Choose Yes, No.

Review missing values and data coding before running. Sample inputs are synthetic teaching examples.

Implementation

Ward agglomerative clustering on numeric Euclidean distances. Cut the hierarchy to the selected count. Linkage nodes are zero-based. Does not support nominal or mixed-type distances. At most 1,000 complete rows. Standardization uses population SD. Assignments, original-unit means and silhouette are exploratory summaries, not p-values or proof of true groups. Synthetic example: 90 simulated observations from three overlapping numeric groups.

• scipy 1.15.3: scipy.cluster.hierarchy.linkage, scipy.cluster.hierarchy.cut_tree

These are pinned library versions; saved results record the versions actually used at runtime.

Library references

• SciPy statistical methods
• statsmodels models and statistical tests
• scikit-learn clustering
• lifelines survival comparisons