Consider a single AN used for classification in a $2$D space with an augmented vector as discussed in the Engelbrecht text. This AN is a summation unit $($SU$)$ and its activation function fAN is a step function with outputs $\backslash$gamma $1=1$ for fAN$($net$)>=0$ and $\backslash$gamma $2=0$ for fAN$($net$)<0.$ Given the weights v$1=1\mathrm{.}0,$ v$2=0\mathrm{.}3,$ and v$3=0\mathrm{.}5,$ draw this AN$.$

Draw $($on graph or engineering paper or by using software$)$ the decision boundary encoded by this AN$.$ Be sure to indicate the $\backslash$gamma $1$ side of the boundary.

Add the following points on the graph you just drew and label the class of each according to the AN$.$

$(1\mathrm{.}0,0\mathrm{.}2)$

$(0\mathrm{.}0,0\mathrm{.}0)$

$(0\mathrm{.}1,0\mathrm{.}5)$

$(1\mathrm{.}7,0\mathrm{.}1)$

$(1\mathrm{.}8,1\mathrm{.}4)$

Assume that the AN$$s classification of each of the points above is correct. List a new labeled data item which, if added to the data set above, would necessarily cause the AN to misclassify at least one data item. $($That is$,$ given this new data item, there would be no set of possible weights that would allow this AN to correctly classify all data items.$)$ Explain why the AN would necessarily misclassify at least one data item.

Explain how the decision boundary for this AN would change if $\backslash$gamma $2$ were changed to $1,$ rather than $0.$

$[$Note for explanatory questions, like this one: To explain the answer, describe what the answer is $$ in this case, what changes $($if any$)$ there are to the decision boundary $$ and also why that is the correct answer $$ in this case that answer would be based on how the value of $\backslash$gamma affects the decision boundary.$]$

Explain how the decision boundary for this AN would change if fAN were changed to be a sigmoidal logistic function.

Explain how the classification of each of the points listed above would change if fAN were a sigmoidal logistic function.