Given the data $(x1={\left[\begin{array}{ccc}2& 5& 3\end{array}\right]}^T,y1=850$;$x2={\left[\begin{array}{ccc}1& 2& 2\end{array}\right]}^T,y2=450$;$x3={\left[\begin{array}{ccc}1& 2& 1\end{array}\right]}^T,y3=300),$ learn the

weights of the linear neuron. Use the gradient$-$descent algorithm to determine the

weights. $($WLO$2$ and WLO$3)$

$($WLO$1)$ Given the data consisting of two classes $($red points and blue points$)$:

Blue: $\{\left[\begin{array}{c}-1\\ -1\end{array}\right],\left[\begin{array}{c}1\\ 1\end{array}\right],\left[\begin{array}{c}2\\ 2\end{array}\right]\},$Red:$\{\left[\begin{array}{c}0\\ -1\end{array}\right],\left[\begin{array}{c}-1\\ 0\end{array}\right],\left[\begin{array}{c}2\\ 1\end{array}\right],\left[\begin{array}{c}1\\ 2\end{array}\right]\}$

a$)$ Can you construct a single perceptron based classifier for the above data?

b$)$ Construct a network consisting of two perceptrons to classify the above data. Determine

the solution by hand. You can initialize the perceptrons whichever way you like.

Write a Python code or a MATLAB code for Question $1.($WLO$2,$ WLO$3).$

Is the problem in Q$1$ a supervised or unsupervised learning problem? Explain your answer.

$($WLO$6)$

$($WLO$4)$ Classify the above data in Question $2$ without using the sigmoid and the

sign$(.)$function$.$ Do you see any difference in the two solutions. You can obtain the

solution either by hand or Python or MATLAB. $($WLO$6),($WLO$5)$

Given the vector determine its class using the perceptron as the

activation function. $($WLO$5)$

$($WLO$5)$ Given the vector $[x_1{x}_2]=[21\mathrm{.}75{]}^T$ determine its class using the weights

obtained in Question $5$ and the sigmoid function. What is the estimated probability

value? What can be the advantage of using a probability value?