# 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.*

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## 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)**

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

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*By [Federico Calò](https://federicocalo.dev) — Software Developer & Technical Writer*