Contenu du cours

Analyse de Cluster

1. Clustering Fundamentals

Introduction to Clustering Clustering Vs Classification Clustering Algorithms and Libraries

2. Core Concepts

Missing Values Handling Categorical Features Encoding Data Normalization Distance Measures Linkages Challenge: Preprocessing the Dataset

3. K-Means

What is K-Means Clustering?How K-Means Algorithm Works?Finding Optimal Number of Clusters Using WSS Finding Optimal Number of Clusters Using Silhouette Score Implementing on Dummy Dataset Implementing on Real Dataset Challenge: Implementing K-Means Clustering

4. Hierarchical Clustering

How Hierarchical Clustering Works?Optimal Number of Clusters Implementing on Dummy Dataset Implementing on Customers Dataset Challenge: Implementing Hierarchical Clustering

5. DBSCAN

Why DBSCAN?How DBSCAN Works?How to Assign Points to the Clusters?Implementing on Dummy Dataset Implementing on Real Dataset Challenge: Implementing DBSCAN

6. GMMs

Problem Statement What is Gaussian Distribution?How GMMs Work?Implementing GMM on Dummy Data Implementing GMM on Real Data Challenge: Implementing Gaussian Mixture Models Conclusion

What is Gaussian Distribution?

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]):


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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()

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

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

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Section 6. Chapitre 2

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