Convergence of the synaptic weights for the elastic net method, and its application

Rahman Ghamasaee, Jeffrey B Goldberg

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Solution procedures for the traveling salesman problem (TSP), i.e. the problem of finding the minimum Hamiltonian circuit in a network of cities, can be divided into two categories: exact methods and approximate (or heuristic) methods. Since TSP is an NP hard problem, good heuristic approaches are of interest. The neural networks heuristic solutions of TSP was initiated by Hopfield and Tank. One such heuristic called the elastic net method is illustrated by the following, an imaginary rubber band is placed at the centroid of the distribution of n cities. Then some finite number (m greater than n) of points (nodes) on this rubber band changes their positions according to the dynamics of the method. Eventually they describe a tour around the cities. We express the dynamics and stability of the elastic net algorithm. We show that if a unique node is converging to a city, then the synaptic strength between them approaches one. Then we generalize to the case where more than one node converges to a city. Furthermore, a typical application that could make use of the elastic net method (e.g. multi-target tracking) will be pointed out for later studies. In order to verify the proof of the concept and the associated theorems, computer simulations were conducted for a reasonable number of cities.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
Pages145-153
Number of pages9
Volume3069
DOIs
StatePublished - 1997
EventAutomatic Target Recognition VII - Orlando, FL, United States
Duration: Apr 22 1997Apr 22 1997

Other

OtherAutomatic Target Recognition VII
CountryUnited States
CityOrlando, FL
Period4/22/974/22/97

Fingerprint

Elastic Net
Traveling salesman problem
Travelling salesman problems
Rubber
traveling salesman problem
Heuristics
Vertex of a graph
Multi-target Tracking
Hamiltonians
Heuristic methods
Hamiltonian circuit
Exact Method
Heuristic Method
NP-hard Problems
Centroid
Target tracking
rubber
Computational complexity
Express
Computer Simulation

Keywords

  • Convergence
  • Elastic net
  • MTT
  • Neural networks
  • TSP

ASJC Scopus subject areas

  • Applied Mathematics
  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Ghamasaee, R., & Goldberg, J. B. (1997). Convergence of the synaptic weights for the elastic net method, and its application. In Proceedings of SPIE - The International Society for Optical Engineering (Vol. 3069, pp. 145-153) https://doi.org/10.1117/12.277099

Convergence of the synaptic weights for the elastic net method, and its application. / Ghamasaee, Rahman; Goldberg, Jeffrey B.

Proceedings of SPIE - The International Society for Optical Engineering. Vol. 3069 1997. p. 145-153.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ghamasaee, R & Goldberg, JB 1997, Convergence of the synaptic weights for the elastic net method, and its application. in Proceedings of SPIE - The International Society for Optical Engineering. vol. 3069, pp. 145-153, Automatic Target Recognition VII, Orlando, FL, United States, 4/22/97. https://doi.org/10.1117/12.277099
Ghamasaee R, Goldberg JB. Convergence of the synaptic weights for the elastic net method, and its application. In Proceedings of SPIE - The International Society for Optical Engineering. Vol. 3069. 1997. p. 145-153 https://doi.org/10.1117/12.277099
Ghamasaee, Rahman ; Goldberg, Jeffrey B. / Convergence of the synaptic weights for the elastic net method, and its application. Proceedings of SPIE - The International Society for Optical Engineering. Vol. 3069 1997. pp. 145-153
@inproceedings{87ff574c26bb42039253a169d04ab288,
title = "Convergence of the synaptic weights for the elastic net method, and its application",
abstract = "Solution procedures for the traveling salesman problem (TSP), i.e. the problem of finding the minimum Hamiltonian circuit in a network of cities, can be divided into two categories: exact methods and approximate (or heuristic) methods. Since TSP is an NP hard problem, good heuristic approaches are of interest. The neural networks heuristic solutions of TSP was initiated by Hopfield and Tank. One such heuristic called the elastic net method is illustrated by the following, an imaginary rubber band is placed at the centroid of the distribution of n cities. Then some finite number (m greater than n) of points (nodes) on this rubber band changes their positions according to the dynamics of the method. Eventually they describe a tour around the cities. We express the dynamics and stability of the elastic net algorithm. We show that if a unique node is converging to a city, then the synaptic strength between them approaches one. Then we generalize to the case where more than one node converges to a city. Furthermore, a typical application that could make use of the elastic net method (e.g. multi-target tracking) will be pointed out for later studies. In order to verify the proof of the concept and the associated theorems, computer simulations were conducted for a reasonable number of cities.",
keywords = "Convergence, Elastic net, MTT, Neural networks, TSP",
author = "Rahman Ghamasaee and Goldberg, {Jeffrey B}",
year = "1997",
doi = "10.1117/12.277099",
language = "English (US)",
volume = "3069",
pages = "145--153",
booktitle = "Proceedings of SPIE - The International Society for Optical Engineering",

}

TY - GEN

T1 - Convergence of the synaptic weights for the elastic net method, and its application

AU - Ghamasaee, Rahman

AU - Goldberg, Jeffrey B

PY - 1997

Y1 - 1997

N2 - Solution procedures for the traveling salesman problem (TSP), i.e. the problem of finding the minimum Hamiltonian circuit in a network of cities, can be divided into two categories: exact methods and approximate (or heuristic) methods. Since TSP is an NP hard problem, good heuristic approaches are of interest. The neural networks heuristic solutions of TSP was initiated by Hopfield and Tank. One such heuristic called the elastic net method is illustrated by the following, an imaginary rubber band is placed at the centroid of the distribution of n cities. Then some finite number (m greater than n) of points (nodes) on this rubber band changes their positions according to the dynamics of the method. Eventually they describe a tour around the cities. We express the dynamics and stability of the elastic net algorithm. We show that if a unique node is converging to a city, then the synaptic strength between them approaches one. Then we generalize to the case where more than one node converges to a city. Furthermore, a typical application that could make use of the elastic net method (e.g. multi-target tracking) will be pointed out for later studies. In order to verify the proof of the concept and the associated theorems, computer simulations were conducted for a reasonable number of cities.

AB - Solution procedures for the traveling salesman problem (TSP), i.e. the problem of finding the minimum Hamiltonian circuit in a network of cities, can be divided into two categories: exact methods and approximate (or heuristic) methods. Since TSP is an NP hard problem, good heuristic approaches are of interest. The neural networks heuristic solutions of TSP was initiated by Hopfield and Tank. One such heuristic called the elastic net method is illustrated by the following, an imaginary rubber band is placed at the centroid of the distribution of n cities. Then some finite number (m greater than n) of points (nodes) on this rubber band changes their positions according to the dynamics of the method. Eventually they describe a tour around the cities. We express the dynamics and stability of the elastic net algorithm. We show that if a unique node is converging to a city, then the synaptic strength between them approaches one. Then we generalize to the case where more than one node converges to a city. Furthermore, a typical application that could make use of the elastic net method (e.g. multi-target tracking) will be pointed out for later studies. In order to verify the proof of the concept and the associated theorems, computer simulations were conducted for a reasonable number of cities.

KW - Convergence

KW - Elastic net

KW - MTT

KW - Neural networks

KW - TSP

UR - http://www.scopus.com/inward/record.url?scp=58749095487&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58749095487&partnerID=8YFLogxK

U2 - 10.1117/12.277099

DO - 10.1117/12.277099

M3 - Conference contribution

AN - SCOPUS:58749095487

VL - 3069

SP - 145

EP - 153

BT - Proceedings of SPIE - The International Society for Optical Engineering

ER -