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This paper proposes an associative memory neural network whose limiting state is the nearest point in a polyhedron from a given input. Two implementations of the proposed associative memory network are presented based on Dykstra's algorithm and a fixed point theorem for nonexpansive mappings. By these implementations, the set of all correctable errors by the network is characterized as a *dual cone* of the polyhedron at each pattern to be memorized, which leads to a simple amplifying technique to improve the error correction capability. It is shown by numerical examples that the proposed associative memory realizes much better error correction performance than the conventional one based on POCS at the expense of the increase of necessary number of iterations in the recalling stage.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.12 pp.2811-2817

- Publication Date
- 1999/12/25

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- PAPER

- Category
- Neural Networks

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Isao YAMADA, Satoshi IINO, Kohichi SAKANIWA, "An Associative Memory Neural Network to Recall Nearest Pattern from Input" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 12, pp. 2811-2817, December 1999, doi: .

Abstract: This paper proposes an associative memory neural network whose limiting state is the nearest point in a polyhedron from a given input. Two implementations of the proposed associative memory network are presented based on Dykstra's algorithm and a fixed point theorem for nonexpansive mappings. By these implementations, the set of all correctable errors by the network is characterized as a *dual cone* of the polyhedron at each pattern to be memorized, which leads to a simple amplifying technique to improve the error correction capability. It is shown by numerical examples that the proposed associative memory realizes much better error correction performance than the conventional one based on POCS at the expense of the increase of necessary number of iterations in the recalling stage.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_12_2811/_p

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@ARTICLE{e82-a_12_2811,

author={Isao YAMADA, Satoshi IINO, Kohichi SAKANIWA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={An Associative Memory Neural Network to Recall Nearest Pattern from Input},

year={1999},

volume={E82-A},

number={12},

pages={2811-2817},

abstract={This paper proposes an associative memory neural network whose limiting state is the nearest point in a polyhedron from a given input. Two implementations of the proposed associative memory network are presented based on Dykstra's algorithm and a fixed point theorem for nonexpansive mappings. By these implementations, the set of all correctable errors by the network is characterized as a *dual cone* of the polyhedron at each pattern to be memorized, which leads to a simple amplifying technique to improve the error correction capability. It is shown by numerical examples that the proposed associative memory realizes much better error correction performance than the conventional one based on POCS at the expense of the increase of necessary number of iterations in the recalling stage.},

keywords={},

doi={},

ISSN={},

month={December},}

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TY - JOUR

TI - An Associative Memory Neural Network to Recall Nearest Pattern from Input

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 2811

EP - 2817

AU - Isao YAMADA

AU - Satoshi IINO

AU - Kohichi SAKANIWA

PY - 1999

DO -

JO - IEICE TRANSACTIONS on Fundamentals

SN -

VL - E82-A

IS - 12

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - December 1999

AB - This paper proposes an associative memory neural network whose limiting state is the nearest point in a polyhedron from a given input. Two implementations of the proposed associative memory network are presented based on Dykstra's algorithm and a fixed point theorem for nonexpansive mappings. By these implementations, the set of all correctable errors by the network is characterized as a *dual cone* of the polyhedron at each pattern to be memorized, which leads to a simple amplifying technique to improve the error correction capability. It is shown by numerical examples that the proposed associative memory realizes much better error correction performance than the conventional one based on POCS at the expense of the increase of necessary number of iterations in the recalling stage.

ER -