### 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) |
---|---|

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) |
---|---|

City | Albuquerque, NM, USA |

Period | 6/4/97 → 6/6/97 |

### ASJC Scopus subject areas

- Control and Systems Engineering

## Cite this

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