Abstract
In this paper, we propose a novel generalized single-hidden layer feedforward network (GSLFN) by employing polynomial functions of inputs as output weights connecting randomly generated hidden units with corresponding output nodes. The main contributions are as follows. For arbitrary N distinct observations with n-dimensional inputs, the augmented hidden node output matrix of the GSLFN with L hidden nodes using any infinitely differentiable activation functions consists of L sub-matrix blocks where each includes n + 1 column vectors. The rank of the augmented hidden output matrix is proved to be no less than that of the SLFN, and thereby contributing to higher approximation performance. Furthermore, under minor constraints on input observations, we rigorously prove that the GLSFN with L hidden nodes can exactly learn L(n + 1) arbitrary distinct observations which is n + 1 times what the SLFN can learn. If the approximation error is allowed, by means of the optimization of output weight coefficients, the GSLFN may require less than N/(n + 1) random hidden nodes to estimate targets with high accuracy. Theoretical results of the GSLFN evidently perform significant superiority to that of SLFNs.
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Wang, N., Han, M., Yu, G., Er, M.J., Meng, F., Sun, S. (2013). Generalized Single-Hidden Layer Feedforward Networks. In: Guo, C., Hou, ZG., Zeng, Z. (eds) Advances in Neural Networks – ISNN 2013. ISNN 2013. Lecture Notes in Computer Science, vol 7951. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39065-4_12
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DOI: https://doi.org/10.1007/978-3-642-39065-4_12
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