Extraction of betti numbers based on a generative model

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

Volumn , Issue , 2012, Pages 537-542

  Maillot, Maxime ^a   Aupetit, Michaël ^a   Govaert, Gerard ^b  

^a DIF   (France)

^b UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEX NETWORKS; LEARNING SYSTEMS; NEURAL NETWORKS; TOPOLOGY;

DATA DISTRIBUTION; ESSENTIAL FEATURES; GENERATIVE MODEL; GEOMETRIC TECHNIQUES; MULTIDIMENSIONAL DATA; NEAREST NEIGHBORS; SIMPLICIAL COMPLEX; TOPOLOGICAL INVARIANTS;

ARTIFICIAL INTELLIGENCE;

EID: 84947801804     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (12)

1. Geoffrey McLachlan and David Peel. In Wiley, editor, Finite Mixture Models, 2000.
2. Teuvo Kohonen. Self-organization and associative memory formation. 1988.
3. Robert Tibshirani. Principal curves revisited. In Springer, editor, Statistics and Computing vol. 2, pages 183-190, 1992.
4. Christopher Bishop, Markus Svensén, and Christopher Williams. The generative topographic mapping. In Neural Computation, pages 215-234, 1998.
5. Michaël Aupetit. Learning topology with the generative gaussian graph and the em algorithm. In MIT Press, editor, Advances in Neural Information Processing Systems, pages 83-90, 2006.
6. Pierre Gaillard, Michaël Aupetit, and Gérard Govaert. Learning topology of a labeled data set with the supervised generative gaussian graph. In Neurocomputing, pages 1283-1299, 2008.
7. Thomas Martinetz and Klaus Schulten. Topology representing networks. In Elsevier London, editor, Neural Networks vol. 7, pages 507-522, 1994.
8. Gunnar Carlsson. Topology and data. pages 255-308, 2009.
9. A. P. Dempster, N. M. Laird, and D. B. Rubin. Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society, SERIES B, pages 1-38, 1977.
10. William Morokoff and Russel Caisch. Quasi-monte carlo integration. In Journal of Computational Physics, pages 218-230, 1995.
11. Gideon Schwarz. Estimating the dimension of a model. In The Annals of Statistics vol. 6, pages 461-464, 1978.
12. Vin de Silva. Plex - a matlab library for studying simplicial homology-comptop.stanford.edu/programs/plex/plexintro.pdf.