Impara High-Dimensional Data and the Curse of Dimensionality

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High-dimensional data has many features, or columns. As you add more dimensions, data points spread farther apart, and the space becomes increasingly empty. This makes it hard to find patterns, because the distances between points lose meaning. This is called the curse of dimensionality — the challenge of analyzing data when there are too many features.


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import numpy as np
import matplotlib.pyplot as plt

# Generate random points in 2D
np.random.seed(0)
points_2d = np.random.rand(100, 2)

# Generate random points in 3D
points_3d = np.random.rand(100, 3)

fig = plt.figure(figsize=(12, 5))

# Plot 2D points
ax1 = fig.add_subplot(1, 2, 1)
ax1.scatter(points_2d[:, 0], points_2d[:, 1], color='blue', alpha=0.6)
ax1.set_title('100 Random Points in 2D')
ax1.set_xlabel('X')
ax1.set_ylabel('Y')

# Plot 3D points
ax2 = fig.add_subplot(1, 2, 2, projection='3d')
ax2.scatter(points_3d[:, 0], points_3d[:, 1], points_3d[:, 2], color='red', alpha=0.6)
ax2.set_title('100 Random Points in 3D')
ax2.set_xlabel('X')
ax2.set_ylabel('Y')
ax2.set_zlabel('Z')

plt.tight_layout()
plt.show()

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Sezione 1. Capitolo 2