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Old 01-25-2013, 01:34 PM
geekoftheweek geekoftheweek is offline
Join Date: Jun 2012
Posts: 26
Default Re: Quick clarification on the growth function

Originally Posted by melipone View Post
In my own words, what I understood is that if no configuration of N points can be shattered (meaning finding a hypothesis for all possible dichotomies), then N is a breakpoint.
I agree with with this. I don't *think* I said something different above.

Originally Posted by melipone View Post
So, in Figure 2.1(b) a configuration of 3 points can be shattered but Figure 2.1(c) gives one example of a configuration of 4 points that cannot be shattered. The catch is that this is just one example. It should not be possible to shatter 4 points in any configuration.
I think we were just meant to infer the rest. The points are placed arbitrarily in that example but if you erected a coordinate system and systematically attempted every configuration of four points they would suffer the same issue: there is a binary configuration that is not separable.
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