Extraction of betti numbers based on a generative model

Maxime Maillot; Michaël Aupetit; Gerard Govaert

Extraction of betti numbers based on a generative model

Maxime Maillot, Michaël Aupetit, Gerard Govaert

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

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 language	English
Title of host publication	ESANN 2012 proceedings, 20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning
Publisher	i6doc.com publication
Pages	537-542
Number of pages	6
ISBN (Print)	9782874190490
Publication status	Published - 2012
Externally published	Yes
Event	20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, ESANN 2012 - Bruges, Belgium Duration: 25 Apr 2012 → 27 Apr 2012

Publication series

Name	ESANN 2012 proceedings, 20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning

Conference

Conference	20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, ESANN 2012
Country/Territory	Belgium
City	Bruges
Period	25/04/12 → 27/04/12

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). (ESANN 2012 proceedings, 20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning). i6doc.com publication.

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 (ESANN 2012 proceedings, 20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning).

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title = "Extraction of betti numbers based on a generative model",

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.",

author = "Maxime Maillot and Micha{\"e}l Aupetit and Gerard Govaert",

note = "Publisher Copyright: {\textcopyright} 2012, i6doc.com publication. All rights reserved.; 20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, ESANN 2012 ; Conference date: 25-04-2012 Through 27-04-2012",

year = "2012",

language = "English",

isbn = "9782874190490",

series = "ESANN 2012 proceedings, 20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning",

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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. 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, 25/04/12.

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 (ESANN 2012 proceedings, 20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning).

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

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N2 - 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.

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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. (ESANN 2012 proceedings, 20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning).

Extraction of betti numbers based on a generative model

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