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. © Springer-Verlag Berlin Heidelberg 2007.
Citation
E. López-Rubio, J. M. Ortiz-de-Lazcano-Lobato, D. López-Rodríguez, et al. “Soft Clustering for Nonparametric Probability Density Function Estimation”. In: Artificial Neural Networks - ICANN 2007, 17th International Conference, Porto, Portugal, September 9-13, 2007, Proceedings, Part I. Ed. by J. M. de á, L. A. Alexandre, W. Duch and D. P. Mandic. Vol. 4668 LNCS. Lecture Notes in Computer Science PART 1. cited By 0; Conference of 17th International Conference on Artificial Neural Networks, ICANN 2007 ; Conference Date: 9 September 2007 Through 13 September 2007; Conference Code:70943. Porto: Springer Verlag, 2007, pp. 707-716. DOI: 10.1007/978-3-540-74690-4_72. URL: https://doi.org/10.1007/978-3-540-74690-4_72.
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- Jesús A. Fajardo, Ricardo Ríos, L. A. Rodríguez (2012). Properties of convergence of a fuzzy set estimator of the density function. Brazilian Journal of Probability and Statistics DOI