### Abstract

A method to analyse recurrent similarities, or self-similarities, in higher dimensional data set, is proposed in this paper. An algorithm capable of solving the inverse problem of building a fractal is detailed. The latter is constituted of three parts: the decomposition of the data into subsets; the determination of a simple IFS from these sets; the reconstruction of the attractor. Basic attractors of fractals are reconstructed using these IFS, with a small error.

Original language | English |
---|---|

Title of host publication | Mendel |

Editors | Matousek Radek |

Publisher | Brno University of Technology |

Pages | 139-146 |

Number of pages | 8 |

ISBN (Electronic) | 9788021438842 |

Publication status | Published - 2009 Jan 1 |

Event | 15th International Conference on Soft Computing: Evolutionary Computation, Genetic Programming, Fuzzy Logic, Rough Sets, Neural Networks, Fractals, Bayesian Methods, MENDEL 2009 - Brno, Czech Republic Duration: 2009 Jun 24 → 2009 Jun 26 |

### Publication series

Name | Mendel |
---|---|

ISSN (Print) | 1803-3814 |

### Other

Other | 15th International Conference on Soft Computing: Evolutionary Computation, Genetic Programming, Fuzzy Logic, Rough Sets, Neural Networks, Fractals, Bayesian Methods, MENDEL 2009 |
---|---|

Country | Czech Republic |

City | Brno |

Period | 09/6/24 → 09/6/26 |

### Keywords

- Data Mining
- Fractals
- Inverse problem
- Iterated Function System
- Neural Network

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)
- Computational Mathematics

## Fingerprint Dive into the research topics of 'Recurrent self-similarities and machine learning: The inverse problem of building fractals'. Together they form a unique fingerprint.

## Cite this

Leleu, T., & Sakurai, A. (2009). Recurrent self-similarities and machine learning: The inverse problem of building fractals. In M. Radek (Ed.),

*Mendel*(pp. 139-146). (Mendel). Brno University of Technology.