Neural Networks with Interval Weights for Nonlinear Mappings of Interval Vectors
Summary :
This paper proposes an approach for approximately realizing nonlinear mappings of interval vectors by interval neural networks. Interval neural networks in this paper are characterized by interval weights and interval biases. This means that the weights and biases are given by intervals instead of real numbers. First, an architecture of interval neural networks is proposed for dealing with interval input vectors. Interval neural networks with the proposed architecture map interval input vectors to interval output vectors by interval arithmetic. Some characteristic features of the nonlinear mappings realized by the interval neural networks are described. Next, a learning algorithm is derived. In the derived learning algorithm, training data are the pairs of interval input vectors and interval target vectors. Last, using a numerical example, the proposed approach is illustrated and compared with other approaches based on the standard back-propagation neural networks with real number weights.
- Publication
- IEICE TRANSACTIONS on Information Vol.E77-D No.4 pp.409-417
- Publication Date
- 1994/04/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- Special Section PAPER (Special Issue on Neurocomputing)
- Category
- Mapping
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Kitaek KWON, Hisao ISHIBUCHI, Hideo TANAKA, "Neural Networks with Interval Weights for Nonlinear Mappings of Interval Vectors" in IEICE TRANSACTIONS on Information,
vol. E77-D, no. 4, pp. 409-417, April 1994, doi: .
Abstract: This paper proposes an approach for approximately realizing nonlinear mappings of interval vectors by interval neural networks. Interval neural networks in this paper are characterized by interval weights and interval biases. This means that the weights and biases are given by intervals instead of real numbers. First, an architecture of interval neural networks is proposed for dealing with interval input vectors. Interval neural networks with the proposed architecture map interval input vectors to interval output vectors by interval arithmetic. Some characteristic features of the nonlinear mappings realized by the interval neural networks are described. Next, a learning algorithm is derived. In the derived learning algorithm, training data are the pairs of interval input vectors and interval target vectors. Last, using a numerical example, the proposed approach is illustrated and compared with other approaches based on the standard back-propagation neural networks with real number weights.
URL: https://global.ieice.org/en_transactions/information/10.1587/e77-d_4_409/_p
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@ARTICLE{e77-d_4_409,
author={Kitaek KWON, Hisao ISHIBUCHI, Hideo TANAKA, },
journal={IEICE TRANSACTIONS on Information},
title={Neural Networks with Interval Weights for Nonlinear Mappings of Interval Vectors},
year={1994},
volume={E77-D},
number={4},
pages={409-417},
abstract={This paper proposes an approach for approximately realizing nonlinear mappings of interval vectors by interval neural networks. Interval neural networks in this paper are characterized by interval weights and interval biases. This means that the weights and biases are given by intervals instead of real numbers. First, an architecture of interval neural networks is proposed for dealing with interval input vectors. Interval neural networks with the proposed architecture map interval input vectors to interval output vectors by interval arithmetic. Some characteristic features of the nonlinear mappings realized by the interval neural networks are described. Next, a learning algorithm is derived. In the derived learning algorithm, training data are the pairs of interval input vectors and interval target vectors. Last, using a numerical example, the proposed approach is illustrated and compared with other approaches based on the standard back-propagation neural networks with real number weights.},
keywords={},
doi={},
ISSN={},
month={April},}
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TY - JOUR
TI - Neural Networks with Interval Weights for Nonlinear Mappings of Interval Vectors
T2 - IEICE TRANSACTIONS on Information
SP - 409
EP - 417
AU - Kitaek KWON
AU - Hisao ISHIBUCHI
AU - Hideo TANAKA
PY - 1994
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E77-D
IS - 4
JA - IEICE TRANSACTIONS on Information
Y1 - April 1994
AB - This paper proposes an approach for approximately realizing nonlinear mappings of interval vectors by interval neural networks. Interval neural networks in this paper are characterized by interval weights and interval biases. This means that the weights and biases are given by intervals instead of real numbers. First, an architecture of interval neural networks is proposed for dealing with interval input vectors. Interval neural networks with the proposed architecture map interval input vectors to interval output vectors by interval arithmetic. Some characteristic features of the nonlinear mappings realized by the interval neural networks are described. Next, a learning algorithm is derived. In the derived learning algorithm, training data are the pairs of interval input vectors and interval target vectors. Last, using a numerical example, the proposed approach is illustrated and compared with other approaches based on the standard back-propagation neural networks with real number weights.
ER -
English
