Assume a Kohonen Network (Self-Organising Map) with two input units and a physical grid of 3 x3=9 output units a, b, c, d, e, f, g, h, i. The weight vectors of the output units are initially given by (shown by their physical arrangement in output space): Wd= - Wa=(1,5) (5, 1) wg (5,5) W = (2.3) We = (3.2) Wh=(3,3) We (4,1) w=(1,4) W = (1, 1) (a) (4 points) The network is presented with an input vector x = (1,7). Which output unit will be the winner and why? (b) (4 points) Assuming a learning rate a = 0.5, what will the weight vector of the winning output be changed to after a single presentation of the input vector x = (1,7)? (c) (4 points) The network from (a) is presented with a large number of inputs where 1 and 2 are chosen randomly from values between 0 and 20. Draw the final state of the network both in (mathematical) input space and in (physical) output space.