### Abstract

In this paper, we analyze convergence properties of the self-organizing feature map (SOFM) with multi-dimensional input using Robbins-Monro stochastic approximation principle. It is shown that the SOFM algorithm optimizes a well defined energy function and converges almost truly (i.e. with probability one) if the input data is from a discrete stochastic distribution. For the case of multi-dimensional inputs generated from continuous distributions, it is shown that the weights of the SOFM algorithm converge almost truly to the centroids of the cells of a Voronoi partition of the input space if the neighborhood function satisfies some reasonable conditions. The density of the weight space in the equilibrium states is also investigated.

Original language | English (US) |
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Title of host publication | Proceedings of the American Control Conference |

Publisher | IEEE |

Pages | 2404-2408 |

Number of pages | 5 |

Volume | 4 |

State | Published - 1997 |

Event | Proceedings of the 1997 American Control Conference. Part 3 (of 6) - Albuquerque, NM, USA Duration: Jun 4 1997 → Jun 6 1997 |

### Other

Other | Proceedings of the 1997 American Control Conference. Part 3 (of 6) |
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City | Albuquerque, NM, USA |

Period | 6/4/97 → 6/6/97 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*Proceedings of the American Control Conference*(Vol. 4, pp. 2404-2408). IEEE.

**Weight convergence and weight density of the multi-dimensional SOFM algorithm.** / Lin, Siming; Si, Jennie.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the American Control Conference.*vol. 4, IEEE, pp. 2404-2408, Proceedings of the 1997 American Control Conference. Part 3 (of 6), Albuquerque, NM, USA, 6/4/97.

}

TY - GEN

T1 - Weight convergence and weight density of the multi-dimensional SOFM algorithm

AU - Lin, Siming

AU - Si, Jennie

PY - 1997

Y1 - 1997

N2 - In this paper, we analyze convergence properties of the self-organizing feature map (SOFM) with multi-dimensional input using Robbins-Monro stochastic approximation principle. It is shown that the SOFM algorithm optimizes a well defined energy function and converges almost truly (i.e. with probability one) if the input data is from a discrete stochastic distribution. For the case of multi-dimensional inputs generated from continuous distributions, it is shown that the weights of the SOFM algorithm converge almost truly to the centroids of the cells of a Voronoi partition of the input space if the neighborhood function satisfies some reasonable conditions. The density of the weight space in the equilibrium states is also investigated.

AB - In this paper, we analyze convergence properties of the self-organizing feature map (SOFM) with multi-dimensional input using Robbins-Monro stochastic approximation principle. It is shown that the SOFM algorithm optimizes a well defined energy function and converges almost truly (i.e. with probability one) if the input data is from a discrete stochastic distribution. For the case of multi-dimensional inputs generated from continuous distributions, it is shown that the weights of the SOFM algorithm converge almost truly to the centroids of the cells of a Voronoi partition of the input space if the neighborhood function satisfies some reasonable conditions. The density of the weight space in the equilibrium states is also investigated.

UR - http://www.scopus.com/inward/record.url?scp=0030652360&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030652360&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0030652360

VL - 4

SP - 2404

EP - 2408

BT - Proceedings of the American Control Conference

PB - IEEE

ER -