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Old 04-21-2013, 09:38 PM
jlaurentum jlaurentum is offline
Join Date: Apr 2013
Location: Venezuela
Posts: 41
Default Positive rays, Positive Intervals, Convex sets and the growth function


From what I understood in lecture 5 as the discussion progresses from positive rays to positive intervals to convex sets, the idea is to put an upper bound on all possible dichotomies. As convex sets, with an upper bound of 2^N on the growth function, are the most general scenario possible, then this is the upperbound on the growth function for perceptrons, which fall somewhere in between the positive ray- positive interval-convex sets continuum. Is my understanding correct?

Due to the political unrest in my country (Venezuela), I've not been able to get started with lecture 6 at this time, so I don't know if what I'm about to ask is addressed later on.

I imagine rotating a perceptron to the point where the boundary line is horizontal and all points fall above or bellow this boundary line:

If this is possible (the rotation), then wouldn't the growth function for linearly separable data with perceptrons be limited to N+1, as in the case of positive rays?
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