Generalized Regularization Networks with a Particular Class of Bell-Shaped Basis Function

Akira NAGAMI; Hirofumi INADA; Takaya MIYANO

Generalized Regularization Networks with a Particular Class of Bell-Shaped Basis Function

Akira NAGAMI, Hirofumi INADA, Takaya MIYANO

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A generalized radial basis function network consisting of (1 + cosh x)^-1 as the basis function of the same class as Gaussian functions is investigated in terms of the feasibility of analog-hardware implementation. A simple way of hardware-implementing (1 + cosh x)^-1 is proposed to generate the exact input-output response curve on an analog circuit constructed with bipolar transistors. To demonstrate that networks consisting of the basis function proposed actually work, the networks are applied to numerical experiments of forecasting chaotic time series contaminated with observational random noise. Stochastic gradient descent is used as learning rule. The networks are capable of learning and making short-term forecasts about the dynamic behavior of the time series with comparable performance to Gaussian radial basis function networks.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E81-A No.11 pp.2443-2448

Publication Date: 1998/11/25

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Category: Neural Networks

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Akira NAGAMI, Hirofumi INADA, Takaya MIYANO, "Generalized Regularization Networks with a Particular Class of Bell-Shaped Basis Function" in IEICE TRANSACTIONS on Fundamentals, vol. E81-A, no. 11, pp. 2443-2448, November 1998, doi: .
Abstract: A generalized radial basis function network consisting of (1 + cosh x)^-1 as the basis function of the same class as Gaussian functions is investigated in terms of the feasibility of analog-hardware implementation. A simple way of hardware-implementing (1 + cosh x)^-1 is proposed to generate the exact input-output response curve on an analog circuit constructed with bipolar transistors. To demonstrate that networks consisting of the basis function proposed actually work, the networks are applied to numerical experiments of forecasting chaotic time series contaminated with observational random noise. Stochastic gradient descent is used as learning rule. The networks are capable of learning and making short-term forecasts about the dynamic behavior of the time series with comparable performance to Gaussian radial basis function networks.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e81-a_11_2443/_p

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@ARTICLE{e81-a_11_2443,
author={Akira NAGAMI, Hirofumi INADA, Takaya MIYANO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Generalized Regularization Networks with a Particular Class of Bell-Shaped Basis Function},
year={1998},
volume={E81-A},
number={11},
pages={2443-2448},
abstract={A generalized radial basis function network consisting of (1 + cosh x)^-1 as the basis function of the same class as Gaussian functions is investigated in terms of the feasibility of analog-hardware implementation. A simple way of hardware-implementing (1 + cosh x)^-1 is proposed to generate the exact input-output response curve on an analog circuit constructed with bipolar transistors. To demonstrate that networks consisting of the basis function proposed actually work, the networks are applied to numerical experiments of forecasting chaotic time series contaminated with observational random noise. Stochastic gradient descent is used as learning rule. The networks are capable of learning and making short-term forecasts about the dynamic behavior of the time series with comparable performance to Gaussian radial basis function networks.},
keywords={},
doi={},
ISSN={},
month={November},}

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TY - JOUR
TI - Generalized Regularization Networks with a Particular Class of Bell-Shaped Basis Function
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2443
EP - 2448
AU - Akira NAGAMI
AU - Hirofumi INADA
AU - Takaya MIYANO
PY - 1998
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E81-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 1998
AB - A generalized radial basis function network consisting of (1 + cosh x)^-1 as the basis function of the same class as Gaussian functions is investigated in terms of the feasibility of analog-hardware implementation. A simple way of hardware-implementing (1 + cosh x)^-1 is proposed to generate the exact input-output response curve on an analog circuit constructed with bipolar transistors. To demonstrate that networks consisting of the basis function proposed actually work, the networks are applied to numerical experiments of forecasting chaotic time series contaminated with observational random noise. Stochastic gradient descent is used as learning rule. The networks are capable of learning and making short-term forecasts about the dynamic behavior of the time series with comparable performance to Gaussian radial basis function networks.
ER -