Extraction of betti numbers based on a generative model

Maxime Maillot, Michaël Aupetit, Gerard Govaert

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Analysis of multidimensional data is challenging. Topological invariants can be used to summarize essential features of such data sets. In this work, we propose to compute the Betti numbers from a generative model based on a simplicial complex learnt from the data. We compare it to the Witness Complex, a geometric technique based on nearest neighbors. Our results on different data distributions with known topology show that Betti numbers are well recovered with our method.

Original languageEnglish
Title of host publicationESANN 2012 proceedings, 20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning
Publisheri6doc.com publication
Pages537-542
Number of pages6
ISBN (Print)9782874190490
Publication statusPublished - 2012
Externally publishedYes
Event20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, ESANN 2012 - Bruges, Belgium
Duration: 25 Apr 201227 Apr 2012

Other

Other20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, ESANN 2012
CountryBelgium
CityBruges
Period25/4/1227/4/12

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Topology

ASJC Scopus subject areas

  • Information Systems
  • Artificial Intelligence

Cite this

Maillot, M., Aupetit, M., & Govaert, G. (2012). Extraction of betti numbers based on a generative model. In ESANN 2012 proceedings, 20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (pp. 537-542). i6doc.com publication.

Extraction of betti numbers based on a generative model. / Maillot, Maxime; Aupetit, Michaël; Govaert, Gerard.

ESANN 2012 proceedings, 20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning. i6doc.com publication, 2012. p. 537-542.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Maillot, M, Aupetit, M & Govaert, G 2012, Extraction of betti numbers based on a generative model. in ESANN 2012 proceedings, 20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning. i6doc.com publication, pp. 537-542, 20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, ESANN 2012, Bruges, Belgium, 25/4/12.
Maillot M, Aupetit M, Govaert G. Extraction of betti numbers based on a generative model. In ESANN 2012 proceedings, 20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning. i6doc.com publication. 2012. p. 537-542
Maillot, Maxime ; Aupetit, Michaël ; Govaert, Gerard. / Extraction of betti numbers based on a generative model. ESANN 2012 proceedings, 20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning. i6doc.com publication, 2012. pp. 537-542
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