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Old 06-16-2012, 01:12 PM
Yellin Yellin is offline
Join Date: Apr 2012
Posts: 26
Default Re: Support vectors in three dimensions

ANSWER (read no further if you want to solve the problem yourself):

There must be at least one event on each of the parallel planes maximizing the margin. Given two fixed points, one on each of two parallel planes, the maximum distance between the planes while keeping them parallel is achieved by rotating them until the normals of the planes are parallel to the vector joining the two points. But that can be done without putting any events between the two planes if and only if there are exactly two support vectors. So two is the minimum number of support vectors. If, at the other extreme, there is no possible orientation change of the parallel planes without a support vector separating from one of them, there must be two more events on the planes, one for each degree of rotational freedom to be prevented. That gives the maximum number of support vectors, four. Any additional event on a plane could only be there with zero probability, because the volume within planes is zero fraction of the cube's volume.
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