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Old 08-24-2015, 08:34 PM
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yaser yaser is offline
Join Date: Aug 2009
Location: Pasadena, California, USA
Posts: 1,478
Default Re: Intuition of the step of PLA

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.
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