Introduction
How do you squeeze data with many dimensions into fewer, without losing what matters? There are two main ideas:
- Projection — flatten the data onto a lower-dimensional flat surface, like casting shadows.
- Manifold learning — recognise that the data lie on a curved surface, and unroll it.
Think of a sheet of paper:
- lying flat on a table but tilted slightly in 3-D space — you can describe every point on it with just 2 coordinates by looking at it from straight above (projection);
- rolled up into a spiral — looking from above squashes different layers on top of each other, so you need to unroll it first (manifold learning).