Computational Intelligence, SS08
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Axis Parallel Rectangles

What is the VC-dimension of axis parallel rectangles in the plane $\mathbb{R}^2$? The target function is specified by a rectangle, and labels any example positive iff it lies inside that rectangle.





VC-dim = 4. For instance the set of points {(1,0),(0.1),(-1,0),(0,-1)} can be shattered, but if you draw the smallest enclosing box around 5 points it is not possible to label the point inside the box - and the remaining points on the edges +.