Yuichi TAMIYA - Fab Futures 2025 - Data Science

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GMM-Based Clustering of Pilgrim Age Group Patterns by year

Prompt(ChatGPT)
Generate Python code to cluster yearly age-group population patterns using a Gaussian Mixture Model.

The input is a CSV file where rows are age groups and columns are years.

Steps required:

• Load the CSV with pandas and set age groups as index
• Transpose the data so that each year is a sample
• Standardize features
• Apply GMM with 3 clusters
• Visualize the results using PCA (2D) and matplotlib
• Label each point with the corresponding year
• Print the estimated GMM means

Use clear comments and best practices.

Answer
The code generaed is below.

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.mixture import GaussianMixture
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA

# ----------------------------------------------------------------------
# STEP 1: Load CSV data
# ----------------------------------------------------------------------

csv_path = "datasets/finalproject/age.csv"
df_age = pd.read_csv(csv_path)

# Set age groups as index
df_age = df_age.set_index("Age_Group")

# Extract year columns only
# Transpose so that each year is a sample and age groups are features
X = df_age.values.T

# ----------------------------------------------------------------------
# STEP 2: Standardization
# ----------------------------------------------------------------------

scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)

# ----------------------------------------------------------------------
# STEP 3: Gaussian Mixture Model (GMM)
# ----------------------------------------------------------------------

n_components = 3
gmm = GaussianMixture(n_components=n_components, random_state=42)
gmm.fit(X_scaled)

labels = gmm.predict(X_scaled)

# ----------------------------------------------------------------------
# STEP 4: PCA visualization
# ----------------------------------------------------------------------

pca = PCA(n_components=2)
X_pca = pca.fit_transform(X_scaled)

plt.figure(figsize=(10, 7))
scatter = plt.scatter(X_pca[:, 0], X_pca[:, 1], c=labels, cmap='viridis', s=100, alpha=0.7)

# Annotate each point with the corresponding year
years = df_age.columns.values
for i, year in enumerate(years):
    plt.annotate(year, (X_pca[i, 0], X_pca[i, 1]), fontsize=9)

plt.title('Density estimation of pilgrim patterns by age group (GMM)')
plt.xlabel('Principal Component 1')
plt.ylabel('Principal Component 2')
plt.colorbar(scatter, label='Estimated density clusters')
plt.grid(True, alpha=0.3)
plt.show()

print("\n--- GMM-based estimation results ---")
print("Estimated means (after standardization):\n", gmm.means_)

--- GMM-based estimation results ---
Estimated means (after standardization):
 [[ 0.59564086  0.81094218  1.00403509]
 [-0.81839126 -0.86224064 -1.10803003]
 [-0.13476914 -0.43535432 -0.49854989]]

Pronpt(ChatGPT)
What dose this result mean?

Answer
The results indicate that yearly pilgrim age distributions can be grouped into several distinct demographic patterns, suggesting structural shifts in age composition rather than a smooth continuous trend.