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Unformatted text preview: Massachusetts Institute of Technology Department of Mechanical Engineering 2.160 Identification, Estimation, and Learning Spring 2006 Problem Set No. 6 Out: April 12, 2006 Due: April 19, 2006 1 Problem 3 An important step in training a radialbasisfunction (RBF) network is to determine the center location and the dilation parameter of each radial basis function so that a limited number of RBF functions may effectively approximate a nonlinear map. 2 Shown below is an example of optimal allocation of RBF functions for voice data processing. Twenty RBF functions are placed optimally for covering approximately 300 data points in 2dimensional input space. The dilation parameter, shown by the radius of each circle, is determined based on the variance of the data classified into the same RBF function. A similar data set has been uploaded to the course site. You are requested to classify these data for the purpose of tuning a RBF network. a). Implement the Generalized Lloyd Algorithm discussed in class for classifying N points of 2dimensional input data into m clusters, i.e. m RBF functions. Download the web site data and test your program with the data. Set m = 9, create an equallyspaced 3 by3 grid in the 2dimensional space, and place the center points of the nine RBF functions initially at those grid points. After optimizing the center locations, compute the dilation parameter for each cluster. Plot the results in the same way as the above example....
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 Spring '06
 HarryAsada
 Mechanical Engineering

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