06 - PCA and Dimensionality Reduction: Compressing Data Intelligently

Compress data while keeping information: PCA finds directions of maximum variance. Eigenvalues of covariance matrix → principal components. Beyond PCA: t-SNE, UMAP for visualization, autoencoders. When to use each, trade-offs: accuracy vs visualization vs interpretability.

What you'll learn

• PCA: projects onto the first k eigenvectors of the covariance matrix
• Eigenvalues \lambda_i: variance captured by each component
• Explained variance: choose k to retain 95%+ of total variance
• Standardization: essential before PCA (scale-sensitive)
• t-SNE/UMAP: for non-linear 2D/3D visualization

This article is part of the Math for AI series on federicocalo.dev.

Read the full article

The complete article (16 min read) with code examples, diagrams, and practical exercises is available here:

➡️ 06 - PCA and Dimensionality Reduction: Compressing Data Intelligently

https://federicocalo.dev/en/blog/pca-dimensionality-reduction-principal-components

By Federico Calò — Software Developer & Technical Writer