UML Gmm

import numpy as np
import matplotlib.pyplot as plt
from sklearn.mixture import GaussianMixture
from sklearn.cluster import KMeans
from sklearn.datasets import make_blobs
from scipy.stats import norm

# Generate synthetic dataset
n_samples = 500
X, y_true = make_blobs(n_samples=n_samples, centers=3, cluster_std=[1.0,2.5,0.5], random_state=42)

# Apply KMeans clustering
kmeans = KMeans(n_clusters=3, random_state=42, n_init=10)
y_kmeans = kmeans.fit_predict(X)

# Apply Gaussian Mixture Model clustering
gmm = GaussianMixture(n_components=3, covariance_type='full', random_state=42)
gmm.fit(X)
y_gmm = gmm.predict(X)

# Visualize KMeans CLustering
plt.figure(figsize=(12, 5))
plt.subplot(1, 2, 1)
plt.scatter(X[:,0], X[:, 1], c=y_kmeans, cmap='viridis', s=30, edgecolors='k')
plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1], c='red', marker='X', s=200, label='Centroids')
plt.title("K-Means Clustering")
plt.xlabel("Feature 1")
plt.ylabel("Feature 2")
plt.legend()
plt.show()

# Visualize Gaussian Mixture Model CLustering
plt.figure(figsize=(12, 5))
plt.subplot(1, 2, 2)
plt.scatter(X[:,0], X[:, 1], c=y_gmm, cmap='viridis', s=30, edgecolors='k')
plt.scatter(gmm.means_[:, 0], gmm.means_[:, 1], c='red', marker='X', s=200, label='GMM Centers')
plt.title("Gaussian Mixture Model Clustering")
plt.xlabel("Feature 1")
plt.ylabel("Feature 2")
plt.legend()
plt.show()

# Plot Gaussian Curves for each component based on the first feature
fig, ax = plt.subplots(figsize=(10, 6))
x_range = np.linspace(X[:,0].min() - 1, X[:, 0].max() + 1, 200)
for i in range(gmm.n_components):
    mean = gmm.means_[i][0]  # Using first feature mean
    std_dev = np.sqrt(gmm.covariances_[i][0, 0])  # Using variance to compute std dev

    # Compute Gaussian probability density function
    y_gaussian = norm.pdf(x_range, mean, std_dev)

    ax.plot(x_range, y_gaussian, label=f"Gaussian {i+1} (μ={mean:.2f}, σ={std_dev:.2f})")
ax.set_title("Gaussian Distributions of GMM Components (Feature 1)")
ax.set_xlabel("Feature 1 Values")
ax.set_ylabel("Probability Density")
ax.legend()
plt.show()