LFD Book Forum Question 9 with triangles
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#1
04-18-2013, 02:41 PM
 Michael Reach Senior Member Join Date: Apr 2013 Location: Baltimore, Maryland, USA Posts: 71
Question 9 with triangles

I am having a hard time finding a good way to visualize this. Maybe someone can make suggestions.

One thing I decided early on: A "best" set of N points (with a maximal number of dichotomies) has to be convex. If it is concave, make the point on the inside -1 and three points surrounding it +1 and it won't work.

Once the set is convex (maybe you can put them on a circle WLOG or some such), I _think_ I can guess the number that will force no breaking, but I don't have a clear argument.
#2
04-18-2013, 02:54 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,478
Re: *ANSWER* Question 9 with triangles

Quote:
 Originally Posted by Michael Reach I am having a hard time finding a good way to visualize this. Maybe someone can make suggestions. One thing I decided early on: A "best" set of N points (with a maximal number of dichotomies) has to be convex. If it is concave, make the point on the inside -1 and three points surrounding it +1 and it won't work. Once the set is convex (maybe you can put them on a circle WLOG or some such), I _think_ I can guess the number that will force no breaking, but I don't have a clear argument.
Take a look at this thread:

and we can discuss this further.
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#3
04-18-2013, 03:59 PM
 Michael Reach Senior Member Join Date: Apr 2013 Location: Baltimore, Maryland, USA Posts: 71
Re: *ANSWER* Question 9 with triangles

Well, I see that an N-gon (won't say which) is easy to shatter, and the (N+2)-gon is easy to see that it can't be shattered. So I know which of the answers to choose, but I'm still not clear on the (N+1)-gon in between.
#4
04-18-2013, 04:28 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,478
Re: Question 9 with triangles

I took out the *ANSWER* warning since the discussion seems safe so far.
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Where everyone thinks alike, no one thinks very much
#5
04-18-2013, 04:48 PM
 Michael Reach Senior Member Join Date: Apr 2013 Location: Baltimore, Maryland, USA Posts: 71
Re: Question 9 with triangles

Ah, well, I guess an (N+1)-gon works too - brute force check on all triangles. Not very elegant, but it works.
#6
04-19-2013, 08:02 AM
 Michael Reach Senior Member Join Date: Apr 2013 Location: Baltimore, Maryland, USA Posts: 71
Re: Question 9 with triangles

I was having about the same troubles figuring out the perceptron problem, but I think looking in the book (*ANSWER*) helps a lot.

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