# Dimensionality Reduction

> ML Prep practice set.

- Stable ID: `dimensionality-reduction`
- Area: machine-learning
- Timebox: 45 minutes

Relate PCA variance objectives to covariance eigenvectors and SVD.

## Instructions

1. Center the data conceptually before applying PCA.

## Ordered items

1. [PCA direction and explained variance](https://mlprep.iwase.dev/item/original-ml-pca/?set=dimensionality-reduction) — `original-ml-pca` (easy, 7 min)
2. [Low-rank error and explained variance](https://mlprep.iwase.dev/item/original-la-low-rank/?set=dimensionality-reduction) — `original-la-low-rank` (medium, 8 min)
3. [Deriving the second principal component](https://mlprep.iwase.dev/item/pml-book1-ex20.3/?set=dimensionality-reduction) — `pml-book1-ex20.3` (hard, 18 min)

## Completion

Explain both reconstruction-error and retained-variance views of PCA.

## Next recommended practice

- [Unsupervised Learning](https://mlprep.iwase.dev/set/unsupervised-learning.md)