The Ridge Function Representation of Polynomials and an Application to Neural Networks

被引：7

作者：

Xie, Ting Fan ^{[1
]}

Cao, Fei Long ^{[1
]}

机构：

[1] China Jiliang Univ, Dept Informat & Math Sci, Hangzhou 310018, Zhejiang, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2011年 / 27卷 / 11期

基金：

中国国家自然科学基金;

关键词：

Ridge function; neural network; polynomial; approximation; UNIVERSAL APPROXIMATION; ERROR-BOUNDS;

D O I：

10.1007/s10114-011-9407-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The first goal of this paper is to establish some properties of the ridge function representation for multivariate polynomials, and the second one is to apply these results to the problem of approximation by neural networks. We find that for continuous functions, the rate of approximation obtained by a neural network with one hidden layer is no slower than that of an algebraic polynomial.

引用

页码：2169 / 2176

页数：8

共 50 条

[31] Application of Neural Networks in Computer Security [J].

Igor, Halenar ;

Bohuslava, Juhasova ;

Martin, Juhas ;

Martin, Nesticky .

24TH DAAAM INTERNATIONAL SYMPOSIUM ON INTELLIGENT MANUFACTURING AND AUTOMATION, 2013, 2014, 69 :1209-1215

[32] Approximation of Fuzzy Neural Networks to Fuzzy-Valued Measurable Function [J].

Li, Jun ;

Gao, Shuai ;

Chen, Bin .

QUANTITATIVE LOGIC AND SOFT COMPUTING 2010, VOL 2, 2010, 82 :351-358

[33] Sensitivity of B-splines Weight Function Neural Networks and Its Application on Signal Recognition [J].

Zhang, Daiyuan .

PROGRESS IN INDUSTRIAL AND CIVIL ENGINEERING, PTS. 1-5, 2012, 204-208 :4962-4966

[34] General Type-2 Fuzzy Membership Function Design and its Application to Neural Networks [J].

Shim, Eun-A ;

Rhee, Frank Chung-Hoon .

IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ 2011), 2011, :479-483

[35] Interpreting Layered Neural Networks via Hierarchical Modular Representation [J].

Watanabe, Chihiro .

NEURAL INFORMATION PROCESSING, ICONIP 2019, PT V, 2019, 1143 :376-388

[36] Approximation with direction basis function neural networks [J].

Cao, WM ;

Feng, H ;

Wang, SJ .

2002 IEEE REGION 10 CONFERENCE ON COMPUTERS, COMMUNICATIONS, CONTROL AND POWER ENGINEERING, VOLS I-III, PROCEEDINGS, 2002, :1290-1293

[37] An investigation of neural networks in thyroid function diagnosis [J].

Zhang G. ;

Berardi V.L. .

Health Care Management Science, 1998, 1 (1) :29-37

[38] Universal approximation with neural networks on function spaces [J].

Kumagai, Wataru ;

Sannai, Akiyoshi ;

Kawano, Makoto .

JOURNAL OF EXPERIMENTAL & THEORETICAL ARTIFICIAL INTELLIGENCE, 2024, 36 (07) :1089-1100

[39] Parabola As an Activation Function of Artificial Neural Networks [J].

Khachumov, M. V. ;

Emelyanova, Yu. G. .

SCIENTIFIC AND TECHNICAL INFORMATION PROCESSING, 2024, 51 (05) :471-477

[40] Function emulation using MVQ neural networks [J].

W. A. Porter ;

A. H. Abouali .

Circuits, Systems and Signal Processing, 1999, 18 :315-329

← 1 2 3 4 5 →