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Old 04-22-2012, 08:01 PM
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htlin htlin is offline
Join Date: Aug 2009
Location: Taipei, Taiwan
Posts: 601
Default Re: Perceptron Learning Algorithm

Originally Posted by shockwavephysics View Post
I have been trying to figure out why updating using w -> w + y_n * x_n works at all. I looked up the relevant section in the text, and there are a series of questions for the student that hint at the answer. I followed that logic to it's conclusion and it does seem to show that updating in that way will always give a w that is better (for the misclassified point) than the previous w. However, I cannot figure out how one comes up with this formulation in the first place. Is there a reference to a derivation I can read?
You can read Problem 1.3 of the recommended textbook, which guides you through a simple proof. Roughly speaking, the proof says the PLA weights get more aligned with the underlying "target weights" after each update.
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