I am confused about the Vapnik-Chervonenkis dimension of a linear separator in 3 dimensions.
In three dimensions, a linear separator would be a plane, and the classification model would be "everything on one side of a plane."
It's apparently proved that the VC dimension of linear separators is d+1, so in 3D, its VC dimension is four. That means it should be able to put any set of 1, 2, 3, or 4 points on one side of a plane.
But, what about this case: four coplanar points on a square with opposite corners same adjacent corners different?
+1 -1 -1 +1
This is the case that a line (2-dimensional linear separator) cannot handle, but the 3-dimensional linear separator is supposed to be able to shatter this. But, I can't see how you could put two corners on "one side of a plane" because all four points are coplanar.
Could someone explain how a 3-d linear separator can shatter the four points I just described?