Imagine flattening the 3D space (Figure 5) down onto the 2D space of the floor.
Then, the image is trying to illustrate which sections of the 2D space have been selected as 'cat' by the classifier (green plane).
Visually, you can imagine that the cat heads have each pushed down a chunk of the green plane (the dog heads have held the green plane up off the ground).
This illustrates that the third dimension was important for separating out the cats: they certainly aren't separated by a clean line in those two dimensions.
However, it also illustrates that the separation might be slightly contrived: looked at in 2D, the green plane seems to have plucked out the odd cats correctly but without logic.
One goal is to show that using a high number of dimensions will guarantee that you can separate dogs and cats, but that this is just an over-fitted solution to the data set that you have: it will not continue to work when you apply it to further data.
> Visually, you can imagine that the cat heads have each pushed down a chunk of the green plane (the dog heads have held the green plane up off the ground).
Thank you, that helps. I was mentally projecting the whole plane down and could see why it wasn't all-green (or all-not).
Imagine flattening the 3D space (Figure 5) down onto the 2D space of the floor.
Then, the image is trying to illustrate which sections of the 2D space have been selected as 'cat' by the classifier (green plane).
Visually, you can imagine that the cat heads have each pushed down a chunk of the green plane (the dog heads have held the green plane up off the ground).
This illustrates that the third dimension was important for separating out the cats: they certainly aren't separated by a clean line in those two dimensions.
However, it also illustrates that the separation might be slightly contrived: looked at in 2D, the green plane seems to have plucked out the odd cats correctly but without logic.
One goal is to show that using a high number of dimensions will guarantee that you can separate dogs and cats, but that this is just an over-fitted solution to the data set that you have: it will not continue to work when you apply it to further data.