(a) The Radial Basis Function Networks (RBFN) can be used to solve regression problems. The output...

 

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(a) The Radial Basis Function Networks (RBFN) can be used to solve regression problems. The output of the radial basis function network is described by y(x)=w,,(|| x ) + b Suppose that you are given a set of pairs of sampling points and desired outputs {(x(i), d(i)), i=1,...,N}. Assume that the parameters (i.e., the centers and widths) of the radial basis units, &,, have already been determined by unsupervised learning. Derive the formula to compute the optimal weights w, and the bias b. When you solve this problem, please try to cope with the issue of over-fitting. Please note that very few marks will be awarded if only the formula is supplied without any mathematical justifications. (15 marks) (b) If the size of the training set is huge (for instance, N>1 million), it might be difficult to use the formula obtained in part (a). Suggest an alternative training algorithm for determining the weights of RBFN to deal with large training set. (5 marks) (c) Give one specific application example where SOM can be used. You cannot use any of the examples discussed in the lecture and the assignment. There is no need to supply the detailed algorithm for SOM, but you need to explain why SOM may be suitable for the particular example you have chosen. (5 marks) (a) The Radial Basis Function Networks (RBFN) can be used to solve regression problems. The output of the radial basis function network is described by y(x)=w,,(|| x ) + b Suppose that you are given a set of pairs of sampling points and desired outputs {(x(i), d(i)), i=1,...,N}. Assume that the parameters (i.e., the centers and widths) of the radial basis units, &,, have already been determined by unsupervised learning. Derive the formula to compute the optimal weights w, and the bias b. When you solve this problem, please try to cope with the issue of over-fitting. Please note that very few marks will be awarded if only the formula is supplied without any mathematical justifications. (15 marks) (b) If the size of the training set is huge (for instance, N>1 million), it might be difficult to use the formula obtained in part (a). Suggest an alternative training algorithm for determining the weights of RBFN to deal with large training set. (5 marks) (c) Give one specific application example where SOM can be used. You cannot use any of the examples discussed in the lecture and the assignment. There is no need to supply the detailed algorithm for SOM, but you need to explain why SOM may be suitable for the particular example you have chosen. (5 marks)