Consider the following two-dimensional pattern recognition problem. Class I contains four points: (1, 1), (0, 1),...

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Consider the following two-dimensional pattern recognition problem. Class I contains four points: (1, 1), (0, 1), (-1, 1) and (0, -1). Class II contains two points: (1, -1), (-1, -1). (a) Is this two-class pattern classification problem linearly separable or nonlinearly separable? Please supply a rigorous mathematical proof for your answer. (8 marks) (b) Design a MLP to separate these two classes completely. You are free to choose any number of hidden layers as well as any number of hidden neurons in each layer. The only constraint is that the activation functions for all the neurons, including the hidden neurons and output neurons, are hard limiters, i.e. step functions. (12 marks) (c) Explain why the MLP designed in (b) can solve this pattern classification problem. (5 marks) Consider the following two-dimensional pattern recognition problem. Class I contains four points: (1, 1), (0, 1), (-1, 1) and (0, -1). Class II contains two points: (1, -1), (-1, -1). (a) Is this two-class pattern classification problem linearly separable or nonlinearly separable? Please supply a rigorous mathematical proof for your answer. (8 marks) (b) Design a MLP to separate these two classes completely. You are free to choose any number of hidden layers as well as any number of hidden neurons in each layer. The only constraint is that the activation functions for all the neurons, including the hidden neurons and output neurons, are hard limiters, i.e. step functions. (12 marks) (c) Explain why the MLP designed in (b) can solve this pattern classification problem. (5 marks)

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a To determine whether the twoclass pattern classification problem is linearly separable or nonlinearly separable we can plot the given points and see ... View the full answer