1 perceptron mistakes 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

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 ${Î¸}^{(0)} = 0$ , 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)

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: $[[{Î¸}_{1}^{(1)}, {Î¸}_{2}^{(1)}], â€¦, [{Î¸}_{1}^{(N)}, {Î¸}_{2}^{(N)}]]$ , where the superscript denotes different $Î¸$ as the separating plane progresses. For example, if $Î¸$ progress from $[0, 0]$ (initialization) to $[1, 2]$ to $[3, âˆ’ 2]$ , you should enter $[[1, 2], [3, âˆ’ 2]]$

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

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Please enter the progression of the separating hyperplane ( $Î¸$ , in the list format described above) of Perceptron algorithm if the algorithm starts with $x^{(1)}$ .

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Please enter the number of mistakes of Perceptron algorithm if the algorithm starts with $x^{(2)}$ .

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Please enter the progression of the separating hyperplane ( $Î¸$ , in the list format described above) of Perceptron algorithm if the algorithm starts with $x^{(2)}$ .

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1. (b)

In part (a), what are the factors that affect the number of mistakes made by the algorithm?

Note: Only choose factors that were changed in part (a), not all factors that can affect the number of mistakes

(Choose all that apply.)

Iteration order

Maximum margin between positive and negative data points

Maximum norm of data points

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1. (c)

Now assume that $x^{(3)} = [âˆ’ 1, 10]$ . How many mistakes does the algorithm make until convergence if cycling starts with data point $x^{(1)}$ ?

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

unanswered

Please enter the progression of the separating hyperplane ( $Î¸$ , in a list format described above) of Perceptron algorithm if the algorithm starts with $x^{(1)}$ .

unanswered

Please enter the number of mistakes of Perceptron algorithm if the algorithm starts with $x^{(2)}$ .

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Please enter the progression of the separating hyperplane ( $Î¸$ , in the list format described above) of Perceptron algorithm if the algorithm starts with $x^{(2)}$ .

unanswered