random projection to O(log n/ε²) dimensions preserves pairwise distances within 1±ε

Can you shrink a 3D object into 2D without losing its shape?

Imagine you're packing a suitcase for a trip, but you want to fit everything in a smaller bag. You don't want to leave out any important items or change how they fit together.

Think of random projection as a magic trick that squishes a 3D object into a 2D space while keeping its shape intact. It's like folding a piece of paper in a way that it still looks like the original shape when you unfold it.

Example

You have a suitcase with 3D objects like a ball, a cube, and a pyramid. Using random projection, you can fold them into a flat 2D paper version that looks like the original 3D shapes.

Remember this

Random projection helps you fit a 3D object into a 2D space without losing its original shape.

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

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