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Old 08-27-2015, 07:43 AM
henry2015 henry2015 is offline
Join Date: Aug 2015
Posts: 31
Default Re: Intuition of the step of PLA

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.
Now, mathematically, I can see why adding y(t) * transpose of x(t) * x(t) to transpose of w(t) * x(t) makes it get closer to the solution. Thanks!

Just a bit hard to visualize it.
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