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• W2118120346 abstract "Smooth hinging hyperplane (SHH) has been proposed as an improvement over the well-known hinging hyperplane (HH) by the fact that it retains the useful features of HH while overcoming HH's drawback of nondifferentiability. This paper introduces a formal characterization of smooth hinge function (SHF), which can be used to generate SHH as a neural network. A method for the general construction of SHF is also given. Furthermore, the work proves that SHH is better than HH in functional approximation, i.e., the optimal error of SHH approximating a general function is always smaller or equal to that of HH. Particularly, in the case that the SHF is generated via the integration of a class of sigmoidal functions, it is further proven that the corresponding SHH of the 2m SHFs would outperform a neural network with m of the sigmoidal function from which the SHF is derived. Any upper bound established on the approximation error of a neural network of m sigmoidal activation functions can hence be translated to the SHH of m SHFs by replacing m with [m/2]. The work also includes an algorithm for the identification of SHH making use of its differentiability property. Simulation experiments are presented to validate the theoretical conclusions to possible extent." @default.
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• W2118120346 date "2010-09-01" @default.
• W2118120346 modified "2023-10-18" @default.
• W2118120346 title "A Neural Network of Smooth Hinge Functions" @default.
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• W2118120346 doi "https://doi.org/10.1109/tnn.2010.2053383" @default.
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