Statistical Summary

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🎯 Purpose

This reference provides statistical tools and interpretation guidelines to evaluate clustering models using both internal metrics and descriptive summaries. It supports unsupervised model inspection, profiling, and stakeholder-ready reporting.

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📐 1. Internal Validation Metrics (No Ground Truth Needed)

✅ Silhouette Score

Measures cohesion vs separation:

• Closer to 1 = better-defined clusters
• 0 = overlapping boundaries
• < 0 = misassignment

from sklearn.metrics import silhouette_score
silhouette_score(X_scaled, cluster_labels)

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✅ Calinski-Harabasz Index

Ratio of between-cluster to within-cluster dispersion:

• Higher is better

from sklearn.metrics import calinski_harabasz_score
calinski_harabasz_score(X_scaled, cluster_labels)

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✅ Davies-Bouldin Index

Average similarity between clusters:

• Lower is better

from sklearn.metrics import davies_bouldin_score
davies_bouldin_score(X_scaled, cluster_labels)

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✅ Within-Cluster Sum of Squares (WCSS)

Used for elbow method in KMeans.

inertia = model.inertia_  # For KMeans

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✅ Average Distance to Centroid

Custom distance-based dispersion metric.

import numpy as np
from sklearn.metrics import pairwise_distances_argmin_min
_, dists = pairwise_distances_argmin_min(model.cluster_centers_, X_scaled)
dists.mean()

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📊 2. Descriptive Cluster Statistics (Per Group)

Summarize cluster structure using standard statistics.

import pandas as pd
X['cluster'] = cluster_labels
X.groupby('cluster').agg(['mean', 'std', 'median', 'min', 'max'])

Metric	Purpose
Mean / Std	Centrality and spread
Min / Max	Range analysis
Count	Cluster size distribution
Median	Robust central tendency

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📋 3. Suggested Summary Table Columns

• Cluster label
• Sample count
• Top 3 distinguishing features (Z-score or absolute mean diff)
• Feature summaries (mean, std)

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🔁 4. Reproducibility & Delta Tracking

• Save centroids or medoids for future comparisons
• Compare distributions over time or version
• Track silhouette or CH index over re-runs

np.save('cluster_centroids_v1.npy', model.cluster_centers_)

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🧪 5. Bonus: Cluster Quality Tiers (Silhouette Guidelines)

Score Range	Interpretation
0.70–1.00	Strong structure
0.50–0.70	Reasonable structure
0.25–0.50	Weak structure
< 0.25	Overlapping or noise-driven

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📦 Reporting Tip

Pair statistical summaries with visual diagnostics (UMAP, silhouette plots, radar charts) for maximum interpretability.

Use this with: Clustering Visual Guide, Checklist, and Decision Card.