Spectral representation of multi-valued functions - 文章详情页

作者：

Zhang, Dezheng (Zhang, Dezheng.) | Jiang, Nan (Jiang, Nan.) | Wulamu, Aziguli (Wulamu, Aziguli.) | Wang, Jing (Wang, Jing.)

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EI Scopus

摘要：

Multi-valued　functions　can　be　compute　by　multi-valued　neural　network.　In　order　to　use　linear　algebra　method　for　analysis　of　multi-valued　function,　this　paper　gives　the　spectral　representation　of　multi-valued　functions.　By　define　a　checksum　function　of　n　variables,　this　paper　gives　an　group　of　orthogonal　bases.　Any　multi-valued　function　in　GF(　p)pn　can　be　uniquely　represented　as　a　linear　combination　of　the　bases.　The　coefficients　are　the　correlations　of　the　multi-valued　function　and　the　bases.　All　the　coefficients　combine　the　generalized　spectrum　of　the　multi-valued　function.　For　a　multi-valued　function　that　can　be　realized　by　a　multi-valued　neuron,　it　is　computable　by　depth-2　polynomial-size　neural　networks.

关键词：

Automation Correlation methods Linear algebra Neural networks Orthogonal functions Process control

作者机构：

[ 1 ] [Zhang, Dezheng]School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China
[ 2 ] [Jiang, Nan]College of Computer Science, Beijing University of Technology, Beijing 100124, China
[ 3 ] [Wulamu, Aziguli]School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China
[ 4 ] [Wang, Jing]School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China

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