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) =1 x(2) =[1,0], y(2) =-1 x(3) =[-1, 1.5], y(3) =1 Given that the algorithm starts with θ(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. 1. (a) 4 points possible (graded) 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 list format: [[θ(1)1,θ(1)2],…,[θ(N)1,θ(N)2]] , where the superscript denotes different θ as the separating plane progresses. For example, if θ progress from [0,0] (initialization) to [1,2] to [3,−2] , you should enter [[1,2],[3,−2]] Please enter the number of mistakes of Perceptron algorithm if the algorithm starts with x(1) .