Problem $2)$ Perceptron Model $(50$ points$)$

Step $1$: Assume a set of exampler patterns in $3-$D space distributed in a cube as shown in the figure below:

$x$ : class $A$

o: class B

$($class A and class B are given in different quadrants$)$

Plot the sampler patterns in a $3-$D graph. Choose approximately $25$ points for each class.

Step $2$: Implement the Perceptron Algorithm. Compute the total error for each exampler set $($i$.$e$.$ for a total of $50$ samples$)$ and plot this error vs$.$ number of epochs $($iterations$).$ Observe the decaying error.

Step $3$: Finding the total weights using the Perceptron algorithm, plot the decision plane in $3$D space showing that this plane can be used for classification of these two classes.