### 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 |
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Title of host publication | Mendel |

Publisher | Brno University of Technology |

Pages | 139-146 |

Number of pages | 8 |

ISBN (Print) | 9788021438842 |

Publication status | Published - 2009 |

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 |

### Other

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

City | Brno |

Period | 09/6/24 → 09/6/26 |

### Fingerprint

### Keywords

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

### Cite this

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

**Recurrent self-similarities and machine learning : The inverse problem of building fractals.** / Leleu, Timothee; Sakurai, Akito.

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

*Mendel.*Brno University of Technology, pp. 139-146, 15th International Conference on Soft Computing: Evolutionary Computation, Genetic Programming, Fuzzy Logic, Rough Sets, Neural Networks, Fractals, Bayesian Methods, MENDEL 2009, Brno, Czech Republic, 09/6/24.

}

TY - GEN

T1 - Recurrent self-similarities and machine learning

T2 - The inverse problem of building fractals

AU - Leleu, Timothee

AU - Sakurai, Akito

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Data Mining

KW - Fractals

KW - Inverse problem

KW - Iterated Function System

KW - Neural Network

UR - http://www.scopus.com/inward/record.url?scp=84907937844&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907937844&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84907937844

SN - 9788021438842

SP - 139

EP - 146

BT - Mendel

PB - Brno University of Technology

ER -