Recurrent self-similarities and machine learning: The inverse problem of building fractals

Timothee Leleu; Akito Sakurai

Recurrent self-similarities and machine learning: The inverse problem of building fractals

Timothee Leleu, Akito Sakurai

Department of Industrial and Systems Engineering

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

1 Citation (Scopus)

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/Territory	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

Cite this

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

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title = "Recurrent self-similarities and machine learning: The inverse problem of building fractals",

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.",

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publisher = "Brno University of Technology",

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AU - Sakurai, Akito

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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.

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KW - Fractals

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KW - Iterated Function System

KW - Neural Network

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M3 - Conference contribution

AN - SCOPUS:84907937844

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BT - Mendel

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PB - Brno University of Technology

Y2 - 24 June 2009 through 26 June 2009

ER -

Recurrent self-similarities and machine learning: The inverse problem of building fractals

Abstract

Publication series

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Keywords

ASJC Scopus subject areas

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