K-means clustering (unsupervised learning algorithm)

An unsupervised machine learning technique called K-Means Clustering assists in assembling data points into clusters according to their innate similarity.K-Mean is utilized when we have unlabeled data and the objective is to find hidden patterns or structures, as opposed to supervised learning, where models are trained using labeled data.

An online retailer, for instance, can divide its clientele into groups like ""Big Spenders," "Frequent Buyers," and "Budget Shoppers" according to their past purchases
"k" stands for the number of clusters or groups into which we wish to divide our objects.

Let's see an example with a sample data..

K-Means Customer Segmentation

Complete step-by-step calculation using 10 customers, 4 independent variables, and K = 3 clusters.

1. Customer Data

We use four independent variables:

• Annual Income — represented in $10,000s
• Annual Spending — represented in $1,000s
• Number of Purchases
• Customer Engagement Score — 1 to 10

Customer	Income	Spending	Purchases	Engagement
C1	2	2	2	2
C2	3	2	2	3
C3	2	3	2	2
C4	3	3	3	3
C5	7	7	7	7
C6	8	7	8	7
C7	7	8	7	8
C8	8	8	8	8
C9	4	9	4	9
C10	5	8	5	9

Each customer is represented as:

Customer = (Income, Spending, Purchases, Engagement)

For example:

C1 = (2, 2, 2, 2)

C9 = (4, 9, 4, 9)

2. Choose the Number of Clusters

For this example:

K = 3

The three groups will eventually be interpreted as:

1. Low-value customers
2. High-value customers
3. High-spending / highly engaged customers

3. Select Initial Centroids

We choose C1, C5, and C9 as the initial centroids.

Centroid 1

M₁ = (2, 2, 2, 2)

Centroid 2

M₂ = (7, 7, 7, 7)

Centroid 3

M₃ = (4, 9, 4, 9)

4. Euclidean Distance Formula

Because there are four independent variables, the distance between a customer and a centroid is:

d = √[(x₁-c₁)² + (x₂-c₂)² + (x₃-c₃)² + (x₄-c₄)²]

Example: C2 → Centroid 1

C2 = (3, 2, 2, 3), and M₁ = (2, 2, 2, 2).

d(C2,M₁) = √[(3-2)² + (2-2)² + (2-2)² + (3-2)²]

= √[1² + 0² + 0² + 1²]

= √2

= 1.414

C2 → Centroid 2

d(C2,M₂) = √[(3-7)² + (2-7)² + (2-7)² + (3-7)²]
= √[16 + 25 + 25 + 16]
= √82
= 9.055

C2 → Centroid 3

d(C2,M₃) = √[(3-4)² + (2-9)² + (2-4)² + (3-9)²]
= √[1 + 49 + 4 + 36]
= √90
= 9.487

C2 is assigned to Cluster 1 because 1.414 is the smallest distance.

5. Iteration 1 — Calculate All Distances

Customer	Distance to M₁	Distance to M₂	Distance to M₃	Assigned Cluster
C1	0.000	10.000	10.296	1
C2	1.414	9.055	9.487	1
C3	1.000	9.539	9.644	1
C4	2.000	8.000	8.602	1
C5	10.000	0.000	5.099	2
C6	11.045	1.414	6.325	2
C7	11.045	1.414	4.472	2
C8	12.000	2.000	5.831	2
C9	10.296	5.099	0.000	3
C10	10.149	3.606	1.732	3

Cluster 1

C1, C2, C3, C4

Cluster 2

C5, C6, C7, C8

Cluster 3

C9, C10

6. Calculate the New Centroid — Cluster 1

Customer	Income	Spending	Purchases	Engagement
C1	2	2	2	2
C2	3	2	2	3
C3	2	3	2	2
C4	3	3	3	3

Income = (2+3+2+3)/4 = 10/4 = 2.50
Spending = (2+2+3+3)/4 = 10/4 = 2.50
Purchases = (2+2+2+3)/4 = 9/4 = 2.25
Engagement = (2+3+2+3)/4 = 10/4 = 2.50

New M₁ = (2.50, 2.50, 2.25, 2.50)

7. Calculate the New Centroid — Cluster 2

Customer	Income	Spending	Purchases	Engagement
C5	7	7	7	7
C6	8	7	8	7
C7	7	8	7	8
C8	8	8	8	8

Income = (7+8+7+8)/4 = 7.50
Spending = (7+7+8+8)/4 = 7.50
Purchases = (7+8+7+8)/4 = 7.50
Engagement = (7+7+8+8)/4 = 7.50

New M₂ = (7.50, 7.50, 7.50, 7.50)

8. Calculate the New Centroid — Cluster 3

Customer	Income	Spending	Purchases	Engagement
C9	4	9	4	9
C10	5	8	5	9

Income = (4+5)/2 = 4.50
Spending = (9+8)/2 = 8.50
Purchases = (4+5)/2 = 4.50
Engagement = (9+9)/2 = 9.00

New M₃ = (4.50, 8.50, 4.50, 9.00)

9. New Centroids After Iteration 1

Cluster	Income	Spending	Purchases	Engagement
Cluster 1	2.50	2.50	2.25	2.50
Cluster 2	7.50	7.50	7.50	7.50
Cluster 3	4.50	8.50	4.50	9.00

10. Iteration 2 — Recalculate Distances

Using the new centroids, we calculate the distances again.

Example: C1 → New M₁

C1 = (2,2,2,2)
M₁ = (2.5,2.5,2.25,2.5)

d = √[(2-2.5)² + (2-2.5)² + (2-2.25)² + (2-2.5)²]
= √[0.25 + 0.25 + 0.0625 + 0.25]
= √0.8125
= 0.901

C1 → New M₂

d = √[(2-7.5)² + (2-7.5)² + (2-7.5)² + (2-7.5)²]
= √121
= 11.000

C1 → New M₃

d = √[(2-4.5)² + (2-8.5)² + (2-4.5)² + (2-9)²]
= √103.75
= 10.186

C1 remains in Cluster 1 because 0.901 is the smallest distance.

11. Iteration 2 — All Distances

Customer	To M₁	To M₂	To M₃	Cluster
C1	0.901	11.000	10.186	1
C2	0.901	10.050	9.314	1
C3	0.901	10.536	9.579	1
C4	1.146	9.000	8.411	1
C5	9.128	1.000	4.330	2
C6	10.189	1.000	5.545	2
C7	10.164	1.000	3.708	2
C8	11.127	1.000	5.074	2
C9	9.477	5.385	0.866	3
C10	9.290	3.873	0.866	3

Convergence: The cluster assignments did not change from Iteration 1 to Iteration 2. Therefore, K-Means has converged for this example.

12. Final Customer Segmentation

Cluster 1 — Low-Value Customers

C1, C2, C3, C4

Centroid: (2.50, 2.50, 2.25, 2.50)

• Low income
• Low spending
• Few purchases
• Low engagement

Possible strategies: discounts, introductory offers, loyalty programs, cross-selling, and engagement campaigns.

Cluster 2 — High-Value Customers

C5, C6, C7, C8

Centroid: (7.50, 7.50, 7.50, 7.50)

• High income
• High spending
• Frequent purchases
• High engagement

Possible strategies: VIP programs, premium products, exclusive offers, early access, and personalized recommendations.

Cluster 3 — High-Spending / Highly Engaged

C9, C10

Centroid: (4.50, 8.50, 4.50, 9.00)

• Moderate income
• Very high spending
• Moderate purchase frequency
• Very high engagement

Possible strategies: premium products, upselling, personalized marketing, subscriptions, and loyalty rewards.

13. Final Results

Customer	Income	Spending	Purchases	Engagement	Final Cluster
C1	2	2	2	2	1
C2	3	2	2	3	1
C3	2	3	2	2	1
C4	3	3	3	3	1
C5	7	7	7	7	2
C6	8	7	8	7	2
C7	7	8	7	8	2
C8	8	8	8	8	2
C9	4	9	4	9	3
C10	5	8	5	9	3

14. Complete K-Means Mathematical Summary

Step 1 — Data Matrix

X = [
(2,2,2,2), (3,2,2,3), (2,3,2,2), (3,3,3,3),
(7,7,7,7), (8,7,8,7), (7,8,7,8), (8,8,8,8),
(4,9,4,9), (5,8,5,9)
]

Step 2 — Choose K

K = 3

Step 3 — Initial Centroids

M₁ = (2,2,2,2)
M₂ = (7,7,7,7)
M₃ = (4,9,4,9)

Step 4 — Distance Calculation

d = √Σ(xⱼ - cⱼ)²

Step 5 — Cluster Assignment

Cluster(Cᵢ) = arg minₖ d(Cᵢ,Mₖ)

Step 6 — Recalculate Centroids

Mₖ = (1/nₖ) Σ Xᵢ

Step 7 — Repeat

Repeat the distance and centroid calculations until the cluster assignments no longer change.

Final result: K-Means converged to 3 customer segments.

15. Business Interpretation

Cluster	Customers	Segment	Business Value
1	C1–C4	Low-value / low engagement	Need nurturing
2	C5–C8	High-value / loyal	Highest priority
3	C9–C10	High spending / highly engaged	Strong upsell opportunity

Important ML concept: K-Means does not inherently know what a "good" or "bad" customer is. It mathematically groups customers based on similarity across the four independent variables. The business meaning of each cluster is interpreted after the clustering is completed.

USE CASE 1: Healthcare Patient Grouping using K-Means Clustering: Hospitals often need to group patients with similar characteristics to: Identify high-risk patients, Personalize treatment plans, Optimize resource allocation, Improve healthcare management

import pandas as pd
from sklearn.preprocessing import StandardScaler
from sklearn.cluster import KMeans

## Load data
#download from
#https://www.pythonplaza.com/healthcare_patient_dataset.html
df = pd.read_csv("patients_data.csv")

# Features used for clustering
X = df[['Age',
        'BMI',
        'Blood_Pressure',
        'Cholesterol',
        'Hospital_Visits']]

# Scale data
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)

# Train model
kmeans = KMeans(n_clusters=3, random_state=42, n_init=10)
kmeans.fit(X_scaled)

# New patient?
new_patient = [[33, 28.0, 139, 210, 4]]

# Apply SAME scaling
new_patient_scaled = scaler.transform(new_patient)

# Predict cluster
cluster = kmeans.predict(new_patient_scaled)

print("Patient belongs to Cluster:", cluster[0])
#Example Output
Patient belongs to Cluster: 1

import pandas as pd
from sklearn.cluster import KMeans
from sklearn.preprocessing import StandardScaler

# ----------------------------------
 # Step 1: Sample Market Basket Data 
# ----------------------------------
data = pd.DataFrame({
    'Customer': ['C001','C002','C003','C004','C005','C006','C007','C008'],
    'Bread': [12,10,11,1,0,2,6,5],
    'Milk': [10,8,9,2,1,1,5,6],
    'Eggs': [8,7,6,1,2,0,4,5],
    'Beer': [0,1,0,10,12,9,4,5],
    'Chips': [1,0,1,8,10,7,3,4]
})

#Load data
#You can also download from
#https://www.pythonplaza.com/sample_customer_shopping.html
data = pd.read_csv("customer_shopping.csv")

print("Original Data")
print(data)

# ----------------------------------
# Step 2: Select Features
# ----------------------------------
X = data[['Bread', 'Milk', 'Eggs', 'Beer', 'Chips']]


# ----------------------------------
# Step 3: Scale Features
# ----------------------------------
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)


# ----------------------------------
# Step 4: Train K-Means Model
# ----------------------------------

kmeans = KMeans(
    n_clusters=3,
    random_state=42,
    n_init=10
)

kmeans.fit(X_scaled)


# ----------------------------------
# Step 5: Assign Clusters
# ----------------------------------

data['Cluster'] = kmeans.labels_

print("\nCluster Assignments")
print(data[['Customer', 'Cluster']])


# ----------------------------------
# Step 6: Cluster Profiles
# ----------------------------------

print("\nCluster Centers (Original Scale)")

centers = scaler.inverse_transform(kmeans.cluster_centers_)

cluster_profiles = pd.DataFrame(
    centers,
    columns=['Bread','Milk','Eggs','Beer','Chips']
)

print(cluster_profiles.round(2))


# ----------------------------------
# Step 7: Test New Customer
# ----------------------------------

new_customer = pd.DataFrame({
    'Bread': [11],
    'Milk': [9],
    'Eggs': [7],
    'Beer': [1],
    'Chips': [1]
})

# Scale using same scaler
new_customer_scaled = scaler.transform(new_customer)

# Predict cluster
predicted_cluster = kmeans.predict(new_customer_scaled)

print("\nNew Customer")
print(new_customer)

print(f"\nPredicted Cluster: {predicted_cluster[0]}")


# ----------------------------------
# Step 8: Recommendation Logic
# ----------------------------------

if predicted_cluster[0] == 0:
    print("Recommendation: Bread, Milk, Eggs promotions")
elif predicted_cluster[0] == 1:
    print("Recommendation: Beer and Chips promotions")
else:
    print("Recommendation: Mixed basket offers")