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henry2015 · #4 08-27-2015, 07:43 AM

Quote:

Originally Posted by yaser

The point ${\bf x}_n$ would be correctly classified if ${\bf w}^{\rm T}{\bf x}_n$ agreed in sign with

. 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

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.