Fuzzy auto-associative neural networks for principal component extraction of noisy data

In this paper, we propose a fuzzy auto-associative neural network for principal component extraction. The objective function is based on reconstructing the inputs from the corresponding outputs of the auto-associative neural network. Unlike the traditional approaches, the proposed criterion is a fuzzy mean squared error. We prove that the proposed objective function is an appropriate fuzzy formulation of auto-associative neural network for principal component extraction. Simulations are given to show the performances of the proposed neural networks in comparison with the existing method.