"Over-Learning" Phenomenon of Wavelet Neural Networks in Remote Sensing Image Classifications with Different Entropy Error Functions

Artificial neural networks are widely applied for prediction, function simulation, and data classification. Among these applications, the wavelet neural network is widely used in image classification problems due to its advantages of high approximation capabilities, fault-tolerant capabilities, learning capacity, its ability to effectively overcome local minimization issues, and so on. The error function of a network is critical to determine the convergence, stability, and classification accuracy of a neural network. The selection of the error function directly determines the network’s performance. Different error functions will correspond with different minimum error values in training samples. With the decrease of network errors, the accuracy of the image classification is increased. However, if the image classification accuracy is difficult to improve upon, or is even decreased with the decreasing of the errors, then this indicates that the network has an “over-learning” phenomenon, which is closely related to the selection of the function errors. With regards to remote sensing data, it has not yet been reported whether there have been studies conducted regarding the “over-learning” phenomenon, as well as the relationship between the “over-learning” phenomenon and error functions. This study takes SAR, hyper-spectral, high-resolution, and multi-spectral images as data sources, in order to comprehensively and systematically analyze the possibility of an “over-learning” phenomenon in the remote sensing images from the aspects of image characteristics and neural network. Then, this study discusses the impact of three typical entropy error functions (NB, CE, and SH) on the “over-learning” phenomenon of a network. The experimental results show that the “over-learning” phenomenon may be caused only when there is a strong separability between the ground features, a low image complexity, a small image size, and a large number of hidden nodes. The SH entropy error function in that case will show a good “over-learning” resistance ability. However, for remote sensing image classification, the “over-learning” phenomenon will not be easily caused in most cases, due to the complexity of the image itself, and the diversity of the ground features. In that case, the NB and CE entropy error network mainly show a good stability. Therefore, a blind selection of a SH entropy error function with a high “over-learning” resistance ability from the wavelet neural network classification of the remote sensing image will only decrease the classification accuracy of the remote sensing image. It is therefore recommended to use an NB or CE entropy error function with a stable learning effect.