$(5)$ The perceptron learning algorithm works like this: In each iteration t$,$ pick a

random x$($t$),$y$($t$)$ and compute the signal s$($t$)=$ wT$($t$)$x$($t$).$ If y$($t$).$s$($t$)<=0,$ update w by w$($t $+1)$ w$($t$)+$ y$($t$).$x$($t$)$;

One may argue that this algorithm does not take the $$closeness$$ between s$($t$)$ and y$($t$)$ into consideration. Let$$s look at another perceptron learning algorithm: In each iteration, pick a random $($x$($t$),$y$($t$))$ and compute s$($t$).$ If y$($t$).$s$($t$)<=1,$ update w by

$)$;

Where $\backslash$eta is a constant. That is$,$ if s$($t$)$ agrees with y$($t$)$ well $($their product is $>1),$ the algorithm does nothing. On the other hand, if s$($t$)$ is further from y$($t$),$ the algorithm changes w$($t$)$ more. In this problem, you are asked to implement this algorithm and study its performance.