Perceptron Mistakes

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Homework due Jun $19,202417$:$29$ IST

In this problem, we will investigate the perceptron algorithm with different iteration ordering.

Consider applying the perceptron algorithm through the origin based on a small training set containing three points:

$x^{(1)}=[-1,-1],$

$x^{(2)}=[1,0],$

$x^{(3)}=[-1,1\mathrm{.}5],$

$y^{(1)}=1$

$y^{(2)}=-1$

$y^{(3)}=1$

Given that the algorithm starts with ${}^{(0)}=0,$ the first point that the algorithm sees is always considered a mistake. The algorithm starts with some data point and then cycles through the data $($in order$)$ until it makes no further mistakes.