Solve the classification problem in Exercise E4.2 by solving inequalities (as in Problem P4.2), and repeat parts (ii) and (iii) with the new solution. (The solution is more difficult than Problem P4.2, since you can’t isolate the weights and biases in a pairwise manner.)
Exercise E4.2
Consider the classification problem defined below.
i. Design a single-neuron perceptron to solve this problem. Design the network graphically, by choosing weight vectors that are orthogonal to the decision boundaries.
ii. Test your solution with all four input vectors.
iii. Classify the following input vectors with your solution. You can either perform the calculations manually or with MATLAB.
iv. Which of the vectors in part (iii) will always be classified the same way, regardless of the solution values for W and b ? Which may vary depending on the solution? Why?
Problem P4.2
Convert the classification problem defined below into an equivalent problem definition consisting of inequalities constraining weight and bias values.
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