We have two categories of vectors. Category I consists of

Category II consists of

We want to train a single-neuron ADALINE network without a bias to recognize these categories (t = 1 for Category I and t = -1 for Category II). Assume that each pattern occurs with equal probability.

i. Draw the network diagram.

ii. Take four steps of the LMS algorithm, using the zero vector as the initial guess. (one pass through the four vectors above - present each vector once). Use a learning rate of 0.1.

iii. What are the optimal weights?

iv. Sketch the optimal decision boundary.

v. How do you think the boundary would change if the network were allowed to have a bias? If the boundary would change, indicate the approximate new position on your sketch of part iv. You do not need to perform any calculations here - just explain your reasoning.