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Old 04-23-2013, 07:07 AM
jlaurentum jlaurentum is offline
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Default d-dimensional Perceptrons and break points (related to Q4 of homework)

Hello:

In slide 9 of lecture 5 (minute 33:03), the Professor gives an example of 3 colinear points for which there can be no possible hypothesis. Still, "it doesn't bother us because we want the maximum bound of possible dichotomies", so k=3 is not considered as a breakpoint. My question is:

In a d-dimensional perceptron, it appears we would not consider a set of points lying in a (d-1)-dimensional hyperplane as candidates for giving an "impossible" dichotomy. Why? Is it because the probability of picking such a set of points from the input space that all lie in a (d-1) dimensional space is zero? (As in the case of picking 3 collinear points in a plane).
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