Lesson 37 of 48
SVD and dimensionality reduction
Throw away most of the numbers and keep almost all of the meaning.
SVD ranks the directions of a matrix by how much they matter, so you can keep the top few and discard the rest. Every embedding, compression and “latent space” you meet is this instinct.
Do this
Compress a greyscale image with the singular value decomposition. Plot reconstruction error against components kept, and report how many you actually needed.
The question that unlocks the next lesson
In an SVD, what do the largest singular values correspond to?
- AThe noisiest directions
- BThe directions carrying the most of the data's variation
- CThe number of rows in the matrix
- DThe directions that are perfectly orthogonal