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$(1)=[-1,-1],$ y$=1$

x$(2)=[1,0],$ y$=-1$

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

Given that the algorithm starts with theta$(0)=0,$ 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.

How many mistakes does the algorithm make until convergence if the algorithm starts with data point x$(1)?$ How many mistakes does the algorithm make if it starts with data point x$(2)?$