t-Distributed Stochastic Neighbor Embedding (t-SNE) Example

This is a simple example of t-Distributed Stochastic Neighbor Embedding (t-SNE) using Python and the scikit-learn library.

t-SNE Overview

t-Distributed Stochastic Neighbor Embedding (t-SNE) is a dimensionality reduction technique that is particularly effective for visualizing high-dimensional data in lower-dimensional spaces. It focuses on preserving pairwise similarities between data points, making it well-suited for capturing the local structure of the data. t-SNE is commonly used for exploratory data analysis and visualization.

Key concepts of t-SNE:

• Pairwise Similarities: Measures of similarity between data points.
• Probabilities: Probability distributions over pairwise similarities in high-dimensional and low-dimensional spaces.
• Kullback-Leibler Divergence: Objective function used to minimize the difference between distributions.

Python Source Code:

# Import necessary libraries
import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import load_digits
from sklearn.manifold import TSNE

# Load a sample dataset (digits dataset)
digits = load_digits()

# Apply t-SNE for dimensionality reduction
tsne = TSNE(n_components=2, random_state=42)
digits_tsne = tsne.fit_transform(digits.data)

# Plot the t-SNE visualization
plt.figure(figsize=(8, 8))
for i in range(10):
    plt.scatter(digits_tsne[digits.target == i, 0], digits_tsne[digits.target == i, 1], label=str(i))

plt.title('t-SNE Visualization of Digits Dataset')
plt.xlabel('t-SNE Dimension 1')
plt.ylabel('t-SNE Dimension 2')
plt.legend()
plt.show()

Explanation:

• Import Libraries: Import necessary Python libraries, including scikit-learn for dimensionality reduction.
• Load Dataset: Load a sample dataset (digits dataset) for demonstration purposes.
• Apply t-SNE: Apply t-SNE for dimensionality reduction with specified parameters (number of components and random state).
• Plot Visualization: Plot the t-SNE visualization of the digits dataset, coloring points based on their digit labels.