1. Train a neuron using the Perceptron Learning Rule, taking:
c = 1
w1 = [0 1 0]t
( x1 = [2 1 -1]t , d1 = -1 )
( x2 = [0 -1 -1]t , d2 = 1 )
Repeat the (x1, d1), (x2, d2) sequence until you obtain the correct outputs. Do not use a computer (except for typing).
2. Implement a classifier for characters L and I using the discrete perceptron learning algorithm. You may use any implementation,
Specifications:
• Use a 3 x 3 binary matrix representation.
• Your neural network should have one neuron.
What happens when the letters are "noisy"?
3. Investigate the use of back-propagation learning using a sigmoidal nonlinearity to achieve one-to-one mappings, as described here:
1. f(x) = 1/x, 1 ≤ x ≤ 100
2. f(x) = log10x, 1 ≤ x ≤ 10
3. f(x) = exp(-x), 1 ≤ x ≤ 10
4. f(x) = sin x, 0 ≤ x ≤ Π/2
For each mapping, do the following:
(a) Set up two sets of data, one for network training, and the other for testing.
(b) Use the training data set to compute the synaptic weights of the network, assumed to have a single hidden layer.
(c) Evaluate the computation accuracy of the network by using the test data.
Use a single hidden layer but with a variable number of hidden neurons. Investigate how the network performance is affected by varying the size of the hidden layer.