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Old 08-27-2015, 02:04 AM
elyakim elyakim is offline
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Join Date: Aug 2015
Posts: 2
Default Re: Intuition of the step of PLA

Quote:
Originally Posted by yaser View Post
The point {\bf x}_n would be correctly classified if {\bf w}^{\rm T}{\bf x}_n agreed in sign with y_n. Therefore, moving {\bf w}^{\rm T}{\bf x}_n in the direction of agreeing with that sign would be moving it in the right direction.

Adding {\bf x}_n y_n to {\bf w} will indeed achieve that, since it will add {\bf x}_n^{\rm T}{\bf x}_n y_n to the quantity {\bf w}^{\rm T}{\bf x}_n and what it adds agrees with y_n in sign since the {\bf x}_n^{\rm T}{\bf x}_n part is always positive.
Earlier I indicated having difficulty with reading the equations in problem 1.3.
It works but I'm concerned I'm updating weights with a rule that is "not so smart":
  • the difference between the target function value and x2 (or the y-value in a visual simulation) for a misclassified point.
Especially I don't recognize the product of "x transpose and x" part.

To summarize my questions:
  1. would insight into vector computation make 'everything easier'?
  2. what is p in the equation? A random symbol?
Thanks again.
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