$4.(20$ pts$)$ Let$$s use an artificial data set to understand the PLA.

A$.$ Generate a linearly separable $2$D data set of size $30.$ Plot the examples $($points blue$/$red based on their

classification$)$ and the target function f $.$ Be sure to add labels to the axes of the plot.

B$.$ Run the PLA on the dataset in $($A$).$ Report the number of updates before the algorithm converges. Plot

the final hypothesis g and f in the same figure. Describe what you see and if the result g is close to f $.$

C$.$ Repeat A$-$B with another randomly generated data set of size $30.$ Compare your results with B$.$

D$.$ Run PLA on a non$-$linearly separable dataset with $10$ points. Again, do steps similar to A$-$B$.$ Decide on

an error to use. Plot the error at each iteration. Run for $30$ iterations. What error metric did you use and

why? Given the plot how would you modify the algorithm to work for non$-$linearly separable datasets?