Compressing with the SVD

A picture as a sum of simple layers

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• The SVD writes any matrix as a sum of rank-one layers ranked by singular values.
• Keeping the top k layers gives the best rank-k approximation: compression.
• Geometrically: rotate, stretch along axes by the singular values, rotate again.

Steps

1. A rank-one picture
2. The singular value decomposition
3. Rebuild the picture
4. What a matrix does
5. Rotate, stretch, rotate
6. Ellipse area
7. The Netflix Prize