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

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

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

x(3) =[-1, 1.5], 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. 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)?

Also provide the progression of the separating plane as the algorithm cycles in the following format: [[(1)1,(1)2],,[(N)1,(N)2]], where the superscript denotes different theta as the separating plane progresses. For example, if progress from [0,0] (initialization) to [1,2] to [3,2], you should enter [[1,2],[3,2]]

1) Please enter the number of mistakes of Perceptron algorithm if the algorithm starts with x(1).

2) Please enter the progression of the separating hyperplane (, in a list format) of Perceptron algorithm if the algorithm starts with x(1).

3) Please enter the number of mistakes of Perceptron algorithm if the algorithm starts with x(2).

4) Please enter the progression of the separating hyperplane (, in a list format) of Perceptron algorithm if the algorithm starts with x(2).