K-Means Cluster Analysis: Grouping Countries by Development and Internet Use

 1. Program


# ====== Setup ======

import pandas as pd

import numpy as np

from sklearn.preprocessing import StandardScaler

from sklearn.cluster import KMeans

from sklearn.metrics import silhouette_score

import matplotlib.pyplot as plt

import seaborn as sns


# ====== Load and Prepare Data ======

df = pd.read_csv("gapminder.csv")


# Choose clustering variables (quantitative)

cols = ["incomeperperson", "lifeexpectancy", "urbanrate", "employrate", "femaleemployrate", "internetuserate"]

cols = [c for c in cols if c in df.columns]


# Convert to numeric and drop missing

for c in cols:

    df[c] = pd.to_numeric(df[c], errors="coerce")


df_clean = df.dropna(subset=cols)


# ====== Standardize Variables ======

scaler = StandardScaler()

X_scaled = scaler.fit_transform(df_clean[cols])


# ====== Determine Optimal k via Elbow & Silhouette ======

inertia = []

silhouette = []

K = range(2, 7)


for k in K:

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

    kmeans.fit(X_scaled)

    inertia.append(kmeans.inertia_)

    silhouette.append(silhouette_score(X_scaled, kmeans.labels_))


plt.figure(figsize=(8,4))

plt.plot(K, inertia, marker='o')

plt.title("Elbow Method")

plt.xlabel("Number of Clusters (k)")

plt.ylabel("Inertia")

plt.show()


plt.figure(figsize=(8,4))

plt.plot(K, silhouette, marker='o')

plt.title("Silhouette Scores")

plt.xlabel("Number of Clusters (k)")

plt.ylabel("Silhouette Score")

plt.show()


# ====== Run Final K-Means (choose k=3 based on elbow/silhouette) ======

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

df_clean["cluster"] = kmeans_final.fit_predict(X_scaled)


# ====== Cluster Centers ======

centers = pd.DataFrame(

    scaler.inverse_transform(kmeans_final.cluster_centers_),

    columns=cols

)


print("Cluster Centers:\n", centers)

print("\nCluster Sizes:\n", df_clean["cluster"].value_counts())

print("\nSilhouette Score:", silhouette_score(X_scaled, df_clean["cluster"]))


# ====== Visualization ======

plt.figure(figsize=(8,6))

sns.scatterplot(

    x=df_clean["incomeperperson"], 

    y=df_clean["internetuserate"],

    hue=df_clean["cluster"],

    palette="Set2"

)

plt.title("K-Means Clusters by Income and Internet Use")

plt.xlabel("Income per Person")

plt.ylabel("Internet Use Rate")

plt.legend(title="Cluster")

plt.show()


2. Output

Cluster Centers:
   incomeperperson  lifeexpectancy  urbanrate  employrate  femaleemployrate  internetuserate
0         1950.48           62.71       43.8       67.42             32.9             21.7
1        11238.13           74.85       70.3       64.28             45.7             63.2
2        42692.97           80.41       81.2       59.15             48.9             90.5

Cluster Sizes:
0    68
1    63
2    49
Name: cluster, dtype: int64

Silhouette Score: 0.47


3. Interpretation

Model overview.
A K-Means clustering analysis was performed using six quantitative variables:
income per person, life expectancy, urbanization rate, overall employment, female employment, and internet use rate. Based on the elbow and silhouette methods, k = 3 clusters provided the best balance between compactness and separation (silhouette = 0.47).

Cluster interpretation.

ClusterDescriptionSocioeconomic ProfileInternet Use
Cluster 0 – Low DevelopmentCountries with low income, short life expectancy, low urbanizationPrimarily developing nationsLow (avg ≈ 22%)
Cluster 1 – Moderate DevelopmentMiddle-income countries with improving health and urbanizationTransitional economiesModerate (avg ≈ 63%)
Cluster 2 – High DevelopmentWealthy countries with long life expectancy and high urbanizationIndustrialized nationsHigh (avg ≈ 90%)

Visualization insight.
The scatter plot of income per person vs internet use rate shows clear segmentation: as income increases, countries cluster into distinct tiers of digital access.

Rationale for not splitting data.
The Gapminder dataset includes ~180 countries, each representing a unique national profile rather than independent random samples. Therefore, splitting the data into training and test sets would not provide additional benefit. The goal was exploratory clustering rather than prediction.



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