Abstract
We present a nonparametric probability density estimation model. The classical Parzen window approach builds a spherical Gaussian density around every input sample. Our method has a first stage where hard neighbourhoods are determined for every sample. Then soft clusters are considered to merge the information coming from several hard neighbourhoods. Our proposal estimates the local principal directions to yield a specific Gaussian mixture component for each soft cluster. This leads to outperform other proposals where local parameter selection is not allowed and/or there are no smoothing strategies, like the manifold Parzen windows.
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References
Bishop, C.: Neural Networks for Pattern Recognition. Oxford University Press, Oxford (1995)
Silverman, B.: Density Estimation for Statistics and Data Analysis. Chapman and Hall, New York (1986)
Vapnik, V.N.: Statistical Learning Theory. John Wiley & Sons, New York (1998)
Izenman, A.J.: Recent developments in nonparametric density estimation. Journal of the American Statistical Association 86(413), 205–224 (1991)
Lejeune, M., Sarda, P.: Smooth estimators of distribution and density functions. Computational Statistics & Data Analysis 14, 457–471 (1992)
Hjort, N.L., Jones, M.C.: Locally Parametric Nonparametric Density Estimation. Annals of Statistics 24(4), 1619–1647 (1996)
Hastie, T., Loader, C.: Local regression: Automatic kernel carpentry. Statistical Science 8, 120–143 (1993)
McLachlan, G., Peel, D.: Finite Mixture Models. Wiley, Chichester (2000)
Parzen, E.: On the Estimation of a Probability Density Function and Mode. Annals of Mathematical Statistics 33, 1065–1076 (1962)
Vincent, P., Bengio, Y.: Manifold Parzen Windows. Advances in Neural Information Processing Systems 15, 825–832 (2003)
Bezdek, J.C.: Numerical taxonomy with fuzzysets. J. Math. Biol. 1, 57–71 (1974)
Tipping, M.E., Bishop, C.M.: Mixtures of Probabilistic Principal Components Analyzers. Neural Computation 11, 443–482 (1999)
Newman, D.J., Hettich, S., Blake, C.L., Merz, C.J.: UCI Repository of machine learning databases. University of California, Department of Information and Computer Science, Irvine, CA (1998), http://www.ics.uci.edu/~mlearn/MLRepository.html
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López-Rubio, E., Ortiz-de-Lazcano-Lobato, J.M., López-Rodríguez, D., del Carmen Vargas-González, M. (2007). Soft Clustering for Nonparametric Probability Density Function Estimation. In: de Sá, J.M., Alexandre, L.A., Duch, W., Mandic, D. (eds) Artificial Neural Networks – ICANN 2007. ICANN 2007. Lecture Notes in Computer Science, vol 4668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74690-4_72
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DOI: https://doi.org/10.1007/978-3-540-74690-4_72
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