Perception learning algorithm implementation $($referring to week $4\text{'}$s tutorial page $16)$ via Python $($Copy

your python program to the answer sheet$).$ Consider a perception in a two$-$dimensional case $(d=2),$

$($a$)$ Generate a linearly separable data set of size $20.$ Plot the examples $(x_n,y_n)$ as well as the target

function $f$ on a plane. Be sure to mark the examples from different classes differently and add labels to

the axes of the plot.

$($b$)$ Run the perceptron learning algorithm on the data set above. Report the number of updates that

the algorithm takes before converging. Plot the examples $(x_n,y_n),$ the target function $f,$ and the final

hypothesis $g$ in the same figure. Comment on whether $f$ is close to $g.$

$($c$)$ Repeat everything in $($b$)$ with another randomly generated data set of size $100.$ Compare your results

with $($b$).$

$($d$)$ Repeat everything in $($b$)$ with another randomly generated data set of size $1,000.$ Compare your

results with $($b$).$

$($e$)$ Modify the algorithm such that it takes $x_{n}in{R}^{10}$ instead of $R^2.$ Randomly generate a linearly

separable data set of size $1,000$ with $x_{n}in{R}^{10}$ and feed the data set to the algorithm. How many

updates does the algorithm take to converge?

$($f$)$ Summarize your conclusions with respect to accuracy and running time as a function of $N$ and $d,$

where $N$ is the size of data set and $d$ is the data dimension.

Hints:

One way to generate a linearly separable data set: first set your own target function, then keep

randomly generating data points and put each of them in the positive or negative class based on the

relation between the data point and the target function.

numpy.random.randint$($low$,$ size$=(N,$dim$)))$: return random integers from the discrete uniform

distribution of the specified dtype in the half$-$open interval $[0,$ low$).$ The output shape is $[$N$,$dim$].$

numpy.random.choice$(a,$ size$=$None, replace$=$True, $p=$ None$)$: generates a random sample from a

given $1-$D array.

Some functions from Python package Matplotlib that may be useful: matplotlib.pyplot.xlabel, mat$-$

plotlib.pyplot.ylabel, matplotlib.pyplot.legend.

It is better to define some functions for perceptron experiments that can be reused in sub$-$questions.