Translated Poisson mixture model for stratification learning

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Translated Poisson mixture model for stratification learning (2000)

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by Gloria Haro , Gregory Randal , Guillermo Sapiro , Gloria Haro , Gregory Randall , Guillermo Sapiro

Venue:	Int. J. Comput. Vision
Citations:	24 - 2 self

BibTeX

@ARTICLE{Haro00translatedpoisson,
    author = {Gloria Haro and Gregory Randal and Guillermo Sapiro and Gloria Haro and Gregory Randall and Guillermo Sapiro},
    title = {Translated Poisson mixture model for stratification learning},
    journal = {Int. J. Comput. Vision},
    year = {2000}
}

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Abstract

A framework for the regularized and robust estimation of non-uniform dimensionality and density in high dimensional noisy data is introduced in this work. This leads to learning stratifications, that is, mixture of manifolds representing different characteristics and complexities in the data set. The basic idea relies on modeling the high dimensional sample points as a process of Translated Poisson mixtures, with regularizing restrictions, leading to a model which includes the presence of noise. The Translated Poisson distribution is useful to model a noisy counting process, and it is derived from the noise-induced translation of a regular Poisson distribution. By maximizing the log-likelihood of the process counting the points falling into a local ball, we estimate the local dimension and density. We show that

Keyphrases

poisson mixture model stratification learning noisy counting process regular poisson distribution basic idea relies translated poisson mixture data set high dimensional noisy data local dimension translated poisson distribution different characteristic high dimensional sample point non-uniform dimensionality local ball robust estimation noise-induced translation

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