What is the curse of dimensionality?

Answer by Kevin Lacker:

Let's say you have a straight line 100 yards long and you dropped a penny somewhere on it. It wouldn't be too hard to find. You walk along the line and it takes two minutes.

Now let's say you have a square 100 yards on each side and you dropped a penny somewhere on it. It would be pretty hard, like searching across two football fields stuck together. It could take days.

Now a cube 100 yards across. That's like searching a 30-story building the size of a football stadium. Ugh.

The difficulty of searching through the space gets a *lot* harder as you have more dimensions. You might not realize this intuitively when it's just stated in mathematical formulas, since they all have the same "width". That's the curse of dimensionality. It gets to have a name because it is unintuitive, useful, and yet simple.

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