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Elroch 04-23-2013 11:08 AM

Multiple perceptron hypotheses
 
Consider the hypothesis set defined by the combination of m perceptrons on an n-dimensional space using the AND operator be denoted H(n,m). i.e. a hypothesis in H(n,m) is defined by m chosen perceptron hypotheses in n-dimensional space all being true.

For example the interior of any tetrahedron in 3-dimensional space is a member of H(3,4), and the set of points (x_1, x_2) such that x_1>2 and x_2>3 is a member of H(2,2)

Let d(n, m) be the VC-dimension of H(n,m)

Which of the following statements is true?
(a) d(8,1) > d(4,2) > d(2,4)
(b) d(8,1) > d(4,2) = d(2,4)
(c) d(8,1) = d(4,2) > d(2,4)
(d) d(8,1) = d(4,2) = d(2,4)
(e) None of the above


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