TW72 UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING MS SYSTEMS ENGINEERING AND ENGINEERING MANAGEMENT SEMESTER 1 EXAMINATION 2015/2016 INTELLIGENT SYSTEMS MODULE NO: EEM7010 Date: Monday 11 th January 2016 Time: 10.00 12.00 INSTRUCTIONS TO CANDIDATES: There are 5 questions. Answer any 3 questions. All questions carry equal marks. Individual marks are shown within the question.
Page 2 of 8 Question 1 This question relates to the supervised neural network a) Describe following two supervised learning algorithms and supported by their algorithm formulae: a back propagation (BP) neural network a Hebbian neural network. b) Consider the two prototype patterns shown in Figure Q1(b). i) Check if these two patterns are orthogonal. (3 marks) ii) Normalise the input P1 (2 marks) iii) Use the Hebb rule to design an autoassociator network that will recognise these two patterns and determine the weight matrix. (6 marks) iv) Find the response of the network to the pattern. (4 marks) P1 P2 Pt Figure Q1(b) PLEASE TURN THE PAGE
Page 3 of 8 Question 2 This question relates to the unsupervised learning neural network a) Compare and contrast the Hebbian unsupervised learning algorithm with competition or the winner-takes-all learning algorithm. b) A Kohonen network receives the input pattern P P = 0.5 0.3 0.8 and with three neurons in the network which have weights W1 = 0.1 0.4, W2 = 0.7 0.9 0.3 0.6, W3 = 0.2 0.5 0. 8 Using the winner-takes-all learning algorithm to determine the neuron that will have its weights adjusted (4 marks) the new values of the weights, suppose that the learning coefficient is 0.3. (3 marks) the architecture of the Kohonen Network (with the assistance of a diagram) and explain its working principles. (8 marks) PLEASE TURN THE PAGE
Page 4 of 8 Question 3 This question relates to a self organising map (SOM) neural network a) Using sketches to identify the difference between a pattern space and a feature space and explain the importance to map a pattern space into a feature space in SOM neural network. (7 marks) b) The details of a 1D mathematical model for self organisation in a system of 8 neurons are given in Appendix 1. Plot by hand the output of neuron s activation function versus the input (net) and discuss the mathematical form for the recursive equations. c) The resulting response for the 1D mathematical model of self organisation in Appendix 1, for a system consisting of 8 neurons is shown below, in Table Q3 (c). In Table Q3 (c), the excitations of all the 8 neurons, for 12 time steps, are presented. Sketch a sequence of graphs, on the same axes, showing the spatial response at subsequent times, for time steps t = (0, 4,12). Discuss how this model displays self organisation? (8 marks) Table Q3 (c) Step y1 y2 y3 y4 y5 y6 y7 y8 0 0.21 0.32 0.43 0.49 0.49 0.43 0.32 0.21 1 0.29 0.61 0.83 0.94 0.94 0.83 0.61 0.29 2 0.30 0.81 1.21 1.38 1.38 1.21 0.81 0.30 3 0.24 0.93 1.55 1.85 1.85 1.55 0.93 0.24 4 0.11 0.94 1.87 2.39 2.39 1.87 0.94 0.11 5 0.00 0.83 2.16 3.00 3.00 2.16 0.83 0.00 6 0.00 0.62 2.39 3.00 3.00 2.39 0.62 0.00 7 0.00 0.63 2.36 3.00 3.00 2.36 0.63 0.00 8 0.00 0.62 2.35 3.00 3.00 2.35 0.62 0.00 9 0.00 0.61 2.35 3.00 3.00 2.35 0.61 0.00 10 0.00 0.60 2.34 3.00 3.00 2.34 0.60 0.00 11 0.00 0.60 2.33 3.00 3.00 2.33 0.60 0.00 12 0.00 0.59 2.33 3.00 3.00 2.33 0.59 0.00 PLEASE TURN THE PAGE
Page 5 of 8 Question 4 This question relates to a self organising map (SOM) neural network a) Discuss the following main aspects of the algorithm for the Kohonen self organising map (SOM) i) the best matching node (BMN) m ii) ii) the neighbourhood (Nm) of the BMN and its spatial extent as training progresses the weight update rule for the SOM iv) the Gaussian form for the learning function = (N i, t) b) The following figure (Figure Q5 (b)) shows the final weights of a selforganising feature map that has been trained for the following conditions: twodimensional input vectors have been uniformly distributed over the triangular area and the self organising array consisted of 15 neurons. Lines between points connect topological neighbours only; points indicate weight coordinates. Sketch the diagram of the network that, in your opinion, has undergone self organisation. Label inputs, neurons, and weights for the computational experiment, results of which are reported on the figure. Suggest the initial weight values that may have been used. (15 marks) Figure Q5 (b) PLEASE TURN THE PAGE
Page 6 of 8 Question 5 This question relates to the application of artificial intelligent neural networks a) Give one application example for using supervised learning and one application example for using unsupervised leaning and Explain their learning and training processes. b) Data for a CMOS heart rate monitoring IC has been taken from 17 production lots with 63 process control parameters (PCMs) logged and a 17 22 SOM used to analyse the correlations in the data. The trained SOM is shown in figure below. Discuss the relationships in the PCMs gleaned from the SOM. (a) Device yield (b) NMOS transistor drain current (c )Aluminium sheet resistance, (d) Metal layer 1 to metal layer 2 contact resistance (e) Production lot numbers. Figure: the component planes for the trained 17 22 SOM illustrating the IC yield dependence on CMOS process control parameters. In the SOM dark gray relates to a small parameter value and light gray to a large value. Question 5 continued over the page
Page 7 of 8 Question 5 continued c) Given the fab uses N type wafers, why, is an abnormal value of the NMOS drain current likely to be a more important than a consideration of the PMOS drain current, in determining IC yield. (5 marks) END OF QUESTIONS
Page 8 of 8 APPENDICES Appendix 1 A 1D Mathematical Model of Self Organisation The response of the i th neuron is given by recursive equation: k 0 y ( t 1) f ( x ( t 1) y ( t) ) i i kk 0 The initial excitation is given by: ik 3 ( i 3) x i ( t) 0.5sin [ ], for i = 1, 2,, 8 15 The neuron s activation function is given by: k 0, net 0 f(net) net, 0 net 3 3, net 3 b = 0.5, c = 0.2 The 1D neural network architecture is shown below and a discretised Mexican top hat function form for the feedback coefficients k. Figure Q3 Question b) (a) The 1D array of neurons. (b) The feedback coefficients k are shown as a function of inter neuronal distance.