Comparisons of Two Learning Strategies for a Supervised Neural Network

Abstract. Artificial neural networks can be used to solve inverse problems. One relevant problem in hydrologic optics is the estimatation of the single scattering albedo from the emitted surface radiation. The multi-layer perceptron (MLP) can be applied to determine the albedo from the measured radiation. The MLP is designed with one hidden layer, where the activation employs the sigmoid function, with backpropagation for set-upping the network parameters. Using the generalized delta rule for the learning process to determine the weight connections, the neural inverse operator (ANN-1) produces good results with 20 inputs (10 incident beams, and 10 emitted beams) and 40 neurons in the hidden layer in two different groups of neurons (30 and 10), with two different parameters for the sigmoid function. The second scheme for training the neural estimator applies the quasi-Newton optimization. For the last strategy, the final neural inverse operator (ANN-2) has 10 inputs (emitted radiation) and 20 neurons in the hidden layer in two different groups of neurons (15 and 5). The measured data were emulated considering five levels of noise. For the generalization test, the ANN-1 and ANN-2 operators obtained 100% of correct answers for the noiseless observational data. For noisy data, the ANN-1 operator obtained 94% of correct answers, while the ANN-2 operator obtained 100% of correct answers. The main difference between these two ANNs is the training method, and the number of neurons in the input and the hidden layer.