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Manifold Constrained Finite Gaussian Mixtures

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Computational Intelligence and Bioinspired Systems (IWANN 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3512))

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Abstract

In many practical applications, the data is organized along a manifold of lower dimension than the dimension of the embedding space. This additional information can be used when learning the model parameters of Gaussian mixtures. Based on a mismatch measure between the Euclidian and the geodesic distance, manifold constrained responsibilities are introduced. Experiments in density estimation show that manifold Gaussian mixtures outperform ordinary Gaussian mixtures.

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References

  1. Parzen, E.: On estimation of a probability density function and mode. Ann. Math. Stat. 33, 1065–1076 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  2. Vincent, P., Bengio, Y.: Manifold Parzen windows. In: Thrun, S., Becker, S., Obermayer, K. (eds.) NIPS 15, pp. 825–832. MIT Press, Cambridge (2003)

    Google Scholar 

  3. McLachlan, G.J., Peel, D.: Finite Mixture Models. Wiley, New York (2000)

    Book  MATH  Google Scholar 

  4. Archambeau, C., Verleysen, M.: From semiparametric to nonparametric density estimation and the regularized Mahalanobis distance (2005) (submitted)

    Google Scholar 

  5. Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. Roy. Stat. Soc., B 39, 1–38 (1977)

    MATH  MathSciNet  Google Scholar 

  6. Lee, J.A., Lendasse, A., Verleysen, M.: Nonlinear projection with curvilinear distances: Isomap versus Curvilinear Distance Analysis. Neurocomputing 57, 49–76 (2003)

    Article  Google Scholar 

  7. Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)

    Article  Google Scholar 

  8. Bernstein, M., de Silva, V., Langford, J., Tenenbaum, J.: Graph approximations to geodesics on embedded manifolds. Techn. report Stanford University, CA (2000)

    Google Scholar 

  9. West, D.B.: Introduction to Graph Theory. Prentice-Hall, Upper Saddle River (1996)

    MATH  Google Scholar 

  10. Dijkstra, E.W.: A note on two problems in connection with graphs. Num. Math. 1, 269–271 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  11. Xu, L., Jordan, M.I.: On convergence properties of the EM algorithm for Gaussian mixtures. Neural Comput. 8, 129–151 (1996)

    Article  Google Scholar 

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© 2005 Springer-Verlag Berlin Heidelberg

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Archambeau, C., Verleysen, M. (2005). Manifold Constrained Finite Gaussian Mixtures. In: Cabestany, J., Prieto, A., Sandoval, F. (eds) Computational Intelligence and Bioinspired Systems. IWANN 2005. Lecture Notes in Computer Science, vol 3512. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494669_100

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  • DOI: https://doi.org/10.1007/11494669_100

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26208-4

  • Online ISBN: 978-3-540-32106-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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