3 An Illustrative Example A iv. Plot the input from part iii in your diagram from part ii, and verify that it falls in the correctly labeled region. E3.5 We want to design a perceptron network to output a 1 when either of these two vectors are input to the network: {1)-9} and to output a -1 when either of the following vectors are input to the net- work: {8-9)- i. Find and sketch a decision boundary for a network that will solve this problem. ii. Find weights and biases that will produce the decision boundary you found in part i. Show all work. iii. Draw the network diagram using abreviated notation. iv. For each of the four vectors given above, calculate the net input, n, and the network output, a, for the network you have designed. Ver- ify that your network solves the problem. v. Are there other weights and biases that would solve the problem? If so, would you consider your weights best? Explain. E3.6 We have the folowing two prototype vectors: {}} i. Find and sketch a decision boundary for a perceptron network that will recognize these two vectors. ii. Find weights and bias that will produce the decision boundary you found in part i. iii. Draw the network diagram using abreviated notation. 3-18 3.1 In this chapter we have designed three different neural networks to distin- guish between apples and oranges, based on three sensor measurements (shape, between bananas and pineapples: = P₁ 1 (Banana) L-1 P₂ = (Pineapple) i. Design a perceptron to recognize these patterns. ii. Design a Hamming network to recognize these patterns. iii. Design a Hopfield network to recognize these patterns. iv. Test the operation of your networks by applying several different in put patterns. Discuss the advantages and disadvantages of each network.