Separable non-linear least-squares minimization-possible improvements for neural net fitting

Neural network minimization problems are often ill-conditioned and in this contribution two ways to handle this will be discussed. It is shown that a better conditioned minimization problem can be obtained if the problem is separated with respect to the linear parameters. This will increase the convergence speed of the minimization. The Levenberg-Marquardt minimization method is often concluded to perform better than the Gauss-Newton and the steepest descent methods on neural network minimization problems. The reason for this is investigated and it is shown that the Levenberg-Marquardt method divides the parameters into two subsets. For one subset the convergence is almost quadratic like that of the Gauss-Newton method, and on the other subset the parameters do hardly converge at all. In this way a fast convergence among the important parameters is obtained