$(30$ points$)$ Below is the pseudo$-$code of perceptron algorithm for binary classification.

Intuitively, this algorithm finds an optimal weight w that can map any input data x

$($e$.$g$.,$ features of a plant$)$ to the corresponding class label y $($e$.$g$.,$ a flower or not$).$ The

subscript t denotes the t$-$th data sample: xt in R

$2$

is the vector of feature values $($real

numbers$)$ and yt $=\backslash$pm $1$ is the class label for the t$-$th sample:

$1.$ w $=$ w$0.$

$2.$ Do Iterate until convergence

$3.$ For each sample $($xt

$,$ yt$),$ t $=1,2,$

$4.$ If yt$$w$,$ xt$<=0$

$5.$ w $=$ w $+$ ytxt

Here $$convergence$$ means weight w does not change at all over one pass through the

entire training dataset in the loop starting in step $3.$ A note on notation: xt denotes

the t$-$th sample in the training data, which is found in the t$-$th row of the matrix X

$($features of all the data samples$).$ yt

is the t$-$th element of the vector y $($labels of all the

data samples$).$ This is the notation used in the textbook. The transpose of a vector

or matrix M is denoted MT with an upper case T$.,$ denotes the dot product.

$($a$)$ Implement three helper functions $($Shown in Table$\mathrm{.}1)$ for the perceptron algorithm

$($MyPerceptron$.$py$)$ and test it on the data provided on the class web site. X in