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Old 04-29-2013, 12:24 PM
Elroch Elroch is offline
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Default Re: VC Dimension and Degrees of Freedom

Another interesting "angle" on them is as (n-1)-dimensional vector subspaces of an n-dimensional vector space without considering the plane x_1=1. This has the same VC-dimension (n) even if the points can be chosen anywhere rather than on the hyperplane x_1=1. Since no points on a ray can be separated, this is essentially the same as them acting on, say, a unit sphere, which has dimension (n-1). Half of this sphere is also the same as our plane x_1=1 by projection along the rays.
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