CANONICAL PIECEWISE-LINEAR APPROXIMATIONS

被引：71
作者：
LIN, JN
UNBEHAUEN, R
机构：
[1] Lehrstuhl fur Allgemeine und Theoretische Elektrotechnik, Universität Erlangen-NUrnberg, D-8520, Erlangen
来源：
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS | 1992年 / 39卷 / 08期
关键词：
D O I：
10.1109/81.168933
中图分类号：
TM [电工技术]; TN [电子技术、通信技术];
学科分类号：
0808 ; 0809 ;
摘要：
In this paper the canonical representation of piecewise-linear functions is considered as a universal approximation scheme of multivariate functions. Meanwhile, two universal approximation schemes in terms of combinations of univariate canonical piecewise-linear functions are proposed. Our discussion supports the application of these schemes in mapping networks, e.g., neural networks or adaptive nonlinear filters.
引用
收藏
页码：697 / 699
页数：3
相关论文
共 11 条
[1]  
[Anonymous], 1985, IMA C ALG APPR FUNCT
[2]   A MULTILAYER NEURAL NETWORK WITH PIECEWISE-LINEAR STRUCTURE AND BACK-PROPAGATION LEARNING [J].
BATRUNI, R .
IEEE TRANSACTIONS ON NEURAL NETWORKS, 1991, 2 (03) :395-403
[3]   CANONICAL PIECEWISE-LINEAR REPRESENTATION [J].
CHUA, LO ;
DENG, AC .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1988, 35 (01) :101-111
[4]   Representation Properties of Networks: Kolmogorov's Theorem Is Irrelevant [J].
Girosi, Federico ;
Poggio, Tomaso .
NEURAL COMPUTATION, 1989, 1 (04) :465-469
[5]   MULTILAYER FEEDFORWARD NETWORKS ARE UNIVERSAL APPROXIMATORS [J].
HORNIK, K ;
STINCHCOMBE, M ;
WHITE, H .
NEURAL NETWORKS, 1989, 2 (05) :359-366
[6]   GLOBAL REPRESENTATION OF MULTIDIMENSIONAL PIECEWISE-LINEAR FUNCTIONS WITH LINEAR PARTITIONS [J].
KANG, SM ;
CHUA, LO .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1978, 25 (11) :938-940
[7]  
KOLMOGOROV AN, 1957, DOKL AKAD NAUK SSSR+, V114, P953
[8]   ADAPTIVE NONLINEAR DIGITAL-FILTER WITH CANONICAL PIECEWISE-LINEAR STRUCTURE [J].
LIN, J ;
UNBEHAUEN, R .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1990, 37 (03) :347-353
[9]  
LIN J, 1992, UNPUB NEURAL COMPUTA
[10]   WHY PIECEWISE LINEAR FUNCTIONS ARE DENSE IN C[0, 1] [J].
SHEKHTMAN, B .
JOURNAL OF APPROXIMATION THEORY, 1982, 36 (03) :265-267
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