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Old 08-29-2012, 08:09 PM
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htlin htlin is offline
Join Date: Aug 2009
Location: Taipei, Taiwan
Posts: 610
Default Re: Problem 2.9 : Growth function of perceptron, seems incorrect

Originally Posted by vsthakur View Post
Sorry for the delayed response here, but i still find that

m_{H}(N) = 2 \sum_{i=0}^d \left({N-1}\atop i\right)

is not the case for a perceptron in d-dimensional space.

When N=6 and d=2, this equation says m_{H}(n) = 32, while i was able to get 38 dichotomies (by picking 6 equidistant points on the circumference of a circle).

If i am missing something, then can you please point me to the proof.

Thank you.
I checked the case you are describing, and the number of dichotomies in the case is 32. (Hint: did you double-calculate the case of 3-positive and 3-negative?) Hope this helps.
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