A committee of MLP with adaptive slope parameter trained by the quasi-Newton method to solve problems in hydrologic optics - Cortivo, F. D.; Chalhoub, E. S.; Campos Velho, Haroldo F. (The 2012 International Joint Conference on Neural Networks (IJCNN), 2012)
Artificial Neural Networks (ANNs) can be used to solve problems in Hydrologic Optics. A relevant problem is the estimation of the single scattering albedo and the phase function parameters, from the emitted radiation at the surface of natural waters. In this work we use a committee of ANNs of Multilayer Perceptron type to perform the estimation of the two mentioned parameters. The training of each network is formulated as a nonlinear optimization problem subject to constraints. In addition, each activation function has a distinct slope parameter, that is initially chosen by a random number generator function. This set of parameter (slopes) was included within the free variables network set in order to be adjusted to reach "optimal values", together with the weights and biases, during the network training. This procedure (slope parameters inclusion) makes each one of the activation functions to have a different slope. Each network that composes the committee was trained independently, in order to become expert for the estimation of only one of the hydrologic parameters. For the networks training, we used the quasi-Newton method that is implemented in E04UCF subroutine, in the NAG library, developed by the Numerical Algorithms Group - NAG. The use of the quasi-Newton method to train the networks together with the distinct slope parameters resulted in a network with a fast learning and excellent generalization. Once the networks were trained, they were grouped so to share the input patterns, but remained independent from one another. For the validation/generalization test we used two distinct sets. For all considered noise levels, we obtained 100% of correct answers for the first set, and above 90% of correct answers for the second set.