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Error analysis and topology modifications of a self-organizing incremental neural network

This paper proposes a mathematical analysis and topological modifications of an online learning method, self-organizing incremental neural network. First, based on investigating its network learning process, the asymptotic mean squared error is derived and the differences in topological structure of its several versions are explained theoretically. Second, considering its shortcomings in determining appropriate threshold regions and inferring insignificant edges, we 1) adopt Gaussian process with an adaptive RBF kernel to generate the probability over the function space of the mapping from the underlying local distribution to neighbouring connection relationships and update the threshold region of each node, and 2) propose a novel model of generalized hyper-geometric ensembles with adaptive dyadic propensities and a modified non-parametric support vector clustering approach. The experimental results on both synthetic data and real-world data sets show that our method generates more even networks with fewer representative nodes and achieves remarkable improvements in terms of accuracy and robustness for complicatedly distributed big data with noise.