Dimensionality Reduction: t-SNE and UMAP

Modern machine learning models operate in extremely high-dimensional spaces.

A single image can contain tens of thousands of pixel values, word embeddings often have hundreds of dimensions, and the hidden layers of deep networks may contain thousands of learned features.

While these high-dimensional representations are powerful, they are also very difficult to interpret, visualize, and analyze directly.

Dimensionality reduction is the process of transforming high-dimensional data into a lower-dimensional space while preserving the most important structure in the data.

By mapping data into two or three dimensions, we can visually explore clusters, analyze class separability, detect outliers, and understand how machine learning models organize information internally.

While Principal Component Analysis (PCA) provides a linear approach to dimensionality reduction, many real-world datasets lie on nonlinear spaces.

To address this, two powerful nonlinear techniques, t-SNE (t-Distributed Stochastic Neighbor Embedding) and UMAP (Uniform Manifold Approximation and Projection), have become standard tools for modern data visualization.