K-Means · Gaussian Mixture · Churn Classification

Subscriber Segmentation
& Churn Console

Six behavioural segments recovered from an unlabelled subscriber base, with a supervised churn model layered on top to quantify the revenue exposure attached to each. The operating point in section 04 is adjustable: precision and recall trade against each other, and the right cut depends on retention budget rather than on any single metric.

00

Executive summary

Where the revenue exposure sits, and what to do about it
01

Data lineage

Full reconciliation from source to model input
Outlier fences use Tukey k=3.0 rather than the default 1.5. On a right-skewed telecom usage distribution the 1.5×IQR fence removes 2–3% of records, most of which are genuine heavy-data subscribers and commercially the most interesting. The wider k=3.0 fence isolates corporate and IoT SIMs specifically. Affected records are winsorised rather than dropped: they represent revenue-generating subscribers and belong in the segment counts, though not at their raw magnitude.
02

Choosing k

Elbow and silhouette both say 5. Business says 6.
Inertia (WCSS) Silhouette
Six segments is a business constraint, not a statistical result. The kneedle elbow and the silhouette peak both indicate k=5. We ship k=6 to match the six distinct offers the campaign supports. The cost of that decision is quantified rather than hidden: silhouette falls from 0.4465 to 0.4156. We judged the additional actionable segment worth a 0.03 separation penalty, and we would revisit the choice if the offer set changed.
03

The six segments

Named by revenue rank for reproducibility
Segment names are derived from revenue rank, not assigned to cluster ids. Mixture-model cluster ids are arbitrary and permute between runs, random seeds and library versions, so a fixed id-to-name mapping would relabel the base whenever any of those changed. Ranking clusters by mean revenue gives a stable, ordered business property to attach names to, which keeps segment definitions reproducible across refreshes.
04

Operating point

Precision and recall trade against each other

Selecting the classification threshold

Held-out test set: subscribers. Each count is computed directly from the model's predicted probabilities at every one of 99 candidate thresholds; no values are interpolated.

0.50
0.01 · flag all0.50 0.99 · flag none
PREDICT STAY
PREDICT CHURN
ACTUAL
STAY
—TRUE NEG
—FALSE POS
ACTUAL
CHURN
—FALSE NEG
—TRUE POS
Customers contacted—
Churners identified—
Churners not identified—
Revenue reachable—
Spent on non-churners—
Precision
—
share of flagged who do churn
Recall
—
share of churners identified
F1
—
harmonic mean of the two
Accuracy
—
see note on class balance
Specificity
—
share of stayers not contacted
ROC-AUC
—
threshold-independent
ROC curve current operating point
Why accuracy is not the headline metric. The base churn rate is , so a model predicting that nobody churns would score accuracy while identifying no churners and protecting no revenue. Moving the dial to 0.99 reproduces exactly that. Precision, recall and PR-AUC () remain informative under this class balance, which is why they lead the reporting.
05

Model selection

Chosen on ROC-AUC, validated on 5-fold CV
Churn drivers
06

Segment surrogate

Deployment fidelity to the mixture model
This figure measures fidelity, not correctness. It reports how closely a fast random forest reproduces the mixture model's own decision boundary, which is what allows new subscribers to be scored in milliseconds without refitting the GMM. Its reference labels come from the GMM, so it should be read as a deployment-fidelity check. Segmentation is unsupervised and therefore has no accuracy in the supervised sense; separation quality is reported in section 02 instead.
07

Control group integrity

The control group is randomised, then verified. A universal control group only supports a causal read of campaign lift if membership is independent of the outcome. Selecting the holdout on any quantity correlated with revenue or engagement — cluster confidence, spend, tenure — produces a control that is not comparable to the treated population, and biases every incrementality estimate computed against it. Here the 3% holdout is drawn at random within each segment, so segment mix is preserved while assignment inside a segment stays independent of behaviour. Balance is then confirmed with standardised mean differences across all covariates; conventional practice treats |SMD| < 0.10 as balanced, and the largest observed value is 0.0216.
08

Sample predictions

Ten unseen subscribers, full scoring path
Every figure on this page is computed from a full pipeline run and read from outputs/dashboard_data.json. Reproduce with stage_a_segment.py → stage_b_predict.py → predict_samples.py → build_dashboard_data.py. Methodology and assumptions are documented in METHODOLOGY.md.