4. Neural networks (a) Figure 4 shows a neuron diagram. The weights are shown next to the respective inputs. Calculate the output of the neuron for input u = [3, -14, -1] and the following activation functions: identity, sigmoid, threshold and polarised threshold. [16] 5 /troi drosodd / turn over 1 -2.0 ui 4.0 U2 V 1.0 -3.0 U3 Figure 4: Diagram of a neuron for problem 4 (a). (b) The left plot of Figure 5 shows a SOM configuration with 16 nodes, labelled as shown. Nodes are considered neighbours if they are joined by a line. The right plot is the scatterplot of the weights in the space of the data. A data point P is shown with a triangle. 11 16 10 11 9 on 8 AP 2 3 7 13 12 8 12 16 6 X2 6 5 4 .14 4 7 11 15 3 3 15 10 2 N 6 10 14 8 1 0 0 1 2 7 8 9 10 11 5 9 3 4 5 6 x1 13 [3] [5] [14] Figure 5: SOM configuration and the weights scatterplot for problem 4 (b). i. Assuming that the SOM is fully trained, show the activation pattern (the output) when P is presented at the input of the SOM. ii. Assuming that the SOM is still in training, which nodes will be updated and why? iii. Assuming that the SOM is still in training, calculate the new weights using a = 0.5. (c) Figure 6 shows an 8-by-8 input image to a convolutional neural network (CNN). The RGB colour values of each pixel are shown vertically within the box of the respective pixel. Suppose that the first layer consists of two filters. Each filter operates on the three colour values of a single pixel. Filter 1 is a median filter, and Filter 2 is a minimum filter. i. Apply step equal to 1 in both directions (rows and columns) and show the output of the convolution layer of the CNN. ii. Apply a max-pooling layer at the output of the convolutional layer and show the result. [6] [6] 59 127 182 115 165 70 133 79 196 73 186 88 18 19 78 15 107 84 44 50 35 188 34 198 181 225 96 62 37 244 100 48 145 123 28 109 188 174 93 22 149 103 127 177 92 86 234 7 Figure 6: Image for the mini-DLNN problem 3 (c)