The **Gaussian distribution** is defined by two key factors: 

- **Mean**: this is the average value and represents the center of the distribution. Most of the data is concentrated near this value;     

- **Standard deviation**: this shows how spread out the data is. A smaller standard deviation means the data is tightly clustered around the mean, while a larger one indicates more spread.

The shape of the Gaussian distribution has some important characteristics: 

- It is **symmetric around the mean**, meaning the left and right sides are mirror images;
 
- About **68%** of the data falls within 1 standard deviation from the mean, **95%** within 2, and **99.7%** within 3. 

This distribution is essential because it models real-world data accurately and serves as the foundation for **Gaussian mixture models**, a flexible approach to solving complex clustering problems. 

Here is the code to create the normal distribution for any data (e.g., `[2, 5, 3, 6, 10, -5]`): 


import numpy as np 
import matplotlib.pyplot as plt 
from scipy.stats import norm 

# Given data
data = [2, 5, 3, 6, 10, -5] 
# Calculate mean and standard deviation
mean = np.mean(data) 
std = np.std(data)
# Generate x values
x = np.linspace(mean - 4 * std, mean + 4 * std, 1000)
# Calculate the normal distribution values
y = norm.pdf(x, mean, std)
# Plot the normal distribution
plt.plot(x, y, label=f"Normal Distribution (mean={mean:.2f}, std={std:.2f})", color='blue')
# Plot the data points as green balls on the x-axis
plt.scatter(data, np.zeros_like(data), color='green', label='Data Points', zorder=5)
plt.grid(True) 
# Display the plot 
plt.show()

What is the key characteristic of the Gaussian distribution? 

Which factor determines the center of a Gaussian distribution?

Le clustering est l'une des techniques fondamentales de l'apprentissage automatique qui vous permet de résoudre de nombreux problèmes complexes dans la vie réelle : segmentation de marché, détection d'anomalies, réduction de la dimensionnalité, révélation de motifs cachés, etc.

Dive into the fundamentals of clustering and discover how it differs from classification. Explore essential algorithms, tools, and libraries that power this unsupervised learning technique to uncover hidden patterns in data.

Gain a solid understanding of key preprocessing techniques that ensure effective clustering. Learn how to handle missing values, encode categorical features, normalize data, and choose appropriate distance measures and linkages to boost clustering accuracy.

Master the skills needed to apply K-Means clustering effectively. Learn how the algorithm works, determine the optimal number of clusters, and gain hands-on experience by implementing K-Means on both synthetic and real-world datasets.

Explore the essentials of hierarchical clustering and learn how to group data into meaningful clusters using dendrograms. Build confidence in identifying the optimal number of clusters and implementing the technique on both synthetic and real-world datasets.

Discover how DBSCAN excels at detecting clusters of varying shapes and handling noise in data. Learn the mechanics behind this density-based algorithm, how to assign points to clusters, and apply it to both synthetic and real datasets with confidence.

Gain a solid understanding of Gaussian Mixture Models and how they use probability to model complex cluster shapes. Learn the principles of Gaussian distribution, explore how GMMs work, and build confidence by applying them to both dummy and real-world data.

Analyse de Cluster

What is Gaussian Distribution?

1. What is the key characteristic of the Gaussian distribution?

2. Which factor determines the center of a Gaussian distribution?