b) A neural network based on a single perceptron neuron is now used to solve the...

 

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b) A neural network based on a single perceptron neuron is now used to solve the following set of inputs and desired outputs training vectors as shown as below. Xi Table 1 Inputs Desired Outputs X2 Y 0 0 0 0 1 1 1 1 0 1 1 1 Use the Perceptron Learning Rule with a SIGN activation function to train this system with the following parameters. Learning rate: Threshold 0.1 0.18 Initial Weights: Bias W₁ = 0.2. w2 = 0.3 0.0 Momentum : 0.0 Determine how many epochs does it take to train this system until all the patterns is accurately learned. Show all your calculations. (8 marks) c) Plot a graph with X₁ on the horizontal axis and X2 on the vertical axis that shows: (i) The four input pairs that have been used to train the system. Indicate clearly on your graph how each input point should be classified. i.e., whether it should be a 0 or a 1. (5 marks) (ii) A straight line that represents the decision boundary that the Perceptron has learnt. Explain how you derived the mathematical equation of this line. (5 marks) b) A neural network based on a single perceptron neuron is now used to solve the following set of inputs and desired outputs training vectors as shown as below. Xi Table 1 Inputs Desired Outputs X2 Y 0 0 0 0 1 1 1 1 0 1 1 1 Use the Perceptron Learning Rule with a SIGN activation function to train this system with the following parameters. Learning rate: Threshold 0.1 0.18 Initial Weights: Bias W₁ = 0.2. w2 = 0.3 0.0 Momentum : 0.0 Determine how many epochs does it take to train this system until all the patterns is accurately learned. Show all your calculations. (8 marks) c) Plot a graph with X₁ on the horizontal axis and X2 on the vertical axis that shows: (i) The four input pairs that have been used to train the system. Indicate clearly on your graph how each input point should be classified. i.e., whether it should be a 0 or a 1. (5 marks) (ii) A straight line that represents the decision boundary that the Perceptron has learnt. Explain how you derived the mathematical equation of this line. (5 marks)

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