K-Means Clustering Lab

K-Means groups patients into K clusters purely from their measurements — no diagnosis labels required. Watch centroids converge step-by-step.

The Algorithm

1. Place K centroids randomly 2. Assign each patient to nearest centroid: cluster(x) = argminₖ ‖x − μₖ‖² 3. Update: μₖ = mean(Cₖ) 4. Repeat 2-3 until convergence WCSS = Σₖ Σxᵢ∈Cₖ ‖xᵢ − μₖ‖² (lower = tighter clusters)

Elbow Method

WCSS always falls as K rises. Choose K at the elbow bend — where additional clusters give diminishing returns.

K too small → underfitting (groups mixed) K too large → overfitting (trivial clusters) K optimal → elbow in WCSS-vs-K curve

⚖️ Ethical Reality

K-Means uses Euclidean distance — so unscaled features (e.g., Glucose in mg/dL vs BMI) distort cluster shapes. Always standardise features before clustering to prevent spurious patient groupings.

① Clustering Configuration

Number of Clusters (K)3

patient subgroups to discover

Patient Cohort Size (N)80

total patients in dataset

② Algorithm Formula

        Assign: c(x)=argminₖ‖x−μₖ‖²
Update: μₖ=(1/|Cₖ|)Σxᵢ
WCSS=Σₖ Σᵢ∈Cₖ ‖xᵢ−μₖ‖²

        Iter: 0
      

x-axis: Fasting Glucose (mg/dL)
y-axis: BMI (kg/m²)
✦ = centroid · colour = cluster

③ Cluster Metrics

Within-Cluster Sum of Squares

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Status

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Iterations

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Avg Cluster Size

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K Used

④ Patient Scatter — colour=cluster · ✦=centroid · Voronoi background=decision regions · watch centroids migrate on Animate

⑤ Elbow Curve — WCSS vs K · highlighted = current K · optimal at elbow bend