Assignment:

Please read the chapter on Perceptrons posted on Canvas.The following problems have been extracted from Notes posted in the Neural Networks Folder. You will notice that the Bias update is treated separately in the Notes. As noted in class you could include the Bias as an input element and augment the pattern and weight vectors accordingly.

1 Consider the classification problem defined below:

i. Draw a diagram of the single-neuron perceptron you would use to solve this problem. How many inputs are required? ii. Draw a graph of the data points, labeled according to their targets. Is this problem solvable with the network you defined in part (i)? Why or why not?

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 ei-ther 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?