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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Parzen, E.: On estimation of a probability density function and mode. Ann. Math. Stat. 33, 1065–1076 (1962)
Vincent, P., Bengio, Y.: Manifold Parzen windows. In: Thrun, S., Becker, S., Obermayer, K. (eds.) NIPS 15, pp. 825–832. MIT Press, Cambridge (2003)
McLachlan, G.J., Peel, D.: Finite Mixture Models. Wiley, New York (2000)
Archambeau, C., Verleysen, M.: From semiparametric to nonparametric density estimation and the regularized Mahalanobis distance (2005) (submitted)
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)
Lee, J.A., Lendasse, A., Verleysen, M.: Nonlinear projection with curvilinear distances: Isomap versus Curvilinear Distance Analysis. Neurocomputing 57, 49–76 (2003)
Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)
Bernstein, M., de Silva, V., Langford, J., Tenenbaum, J.: Graph approximations to geodesics on embedded manifolds. Techn. report Stanford University, CA (2000)
West, D.B.: Introduction to Graph Theory. Prentice-Hall, Upper Saddle River (1996)
Dijkstra, E.W.: A note on two problems in connection with graphs. Num. Math. 1, 269–271 (1959)
Xu, L., Jordan, M.I.: On convergence properties of the EM algorithm for Gaussian mixtures. Neural Comput. 8, 129–151 (1996)
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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
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