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标题：Approach of The Hungarian Geoid Surface with Sequence of Neural Networks
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作者：P. Zaletnyik ; L. Völgyesi ; B. Paláncz 等
期刊名称：ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences
印刷版ISSN：2194-9042
电子版ISSN：2194-9050
出版年度：2004
卷号：XXXV Part B8
页码：119-122
出版社：Copernicus Publications
摘要：For global data representation, like the approximation of a surface, algebraic or trigonometric polynomials may be used. However, polynomial approaches are limited concerning their accuracy. In the last decade neural networks were applied very successfully in many fields of data mining and representation. In this research sequence of neural networks has been employed to high accuracy regression in 3D as data representation in form z = f(x,y). The first term of this series of networks estimates the values of the dependent variable as it is usual, while the second term estimates the error of the first network, the third term estimates the error of the second network and so on. Assuming that the relative error of every network in this sequence is less than 100%, the sum of the estimated error can be reduced very significantly and effectively. To illustrate this method the geoid of Hungary was estimated. To approach this surface, a RBF neural network has been employed with 35 neurons having Gaussian activation functions. We used this type of network, because the radial basis type activation function proved to be the most efficient in case of function approximation problems. According to our experience, the iteration process is converging rapidly, and after 3-4 iteration steps there were no further significant change in the values. Comparing the results of the first network with the fourth network the value of standard deviations was reduced with about 30 percents. And comparing these results with the polynomial approach the improvement is more significant, it is about 60 percents. These computations were carried out with the symbolic-numeric integrated system Mathematica
关键词：Neural; Artificial Intelligence; Surface; Data Mining; Geodesy