3. Radial Basis Functions and Regularization (a) Generate a set of data (of size N = 10) by sampling the function A(x) =0.5+0.4sin(2xx) + 6, where r is a random variable uniformly distributed in [0, 1],c is a Gaussian noise with zero mean and variance equal to 0.1. (2 marks) 2 (b) Implement the radial basis function network with Gaussian Kernels to perform the regression of the data set created in item a). (15 marks) (c) Plot the data set. the function implementing the regression and the generating function y(2) =0.5 + 0.4sin(2xz). (3marks) (d) Construct a second data set, with the same properties as the one cre- ated in item a), but with A = 100 samples. Implement a radial basis function network with Gaussian Kernels. Consider only 10 compo- ments. How are you going to sellect the Kernels centres? Plot the curve obtained and the complete data set and discuss your results. (10 marks) (e) Implement the Poggio and Girossi regularization scheme on the data set constructed in item a). Plot the regularized curve (for a suitable regularization parameter) and the data points. Discuss your results. (20 marks)