Modeling and Unsupervised Classification of Multivariate Hidden Markov Chains With Copulas

@article{Brunel2010ModelingAU,
  title={Modeling and Unsupervised Classification of Multivariate Hidden Markov Chains With Copulas},
  author={Nicolas J.-B. Brunel and J{\'e}r{\^o}me Lapuyade-Lahorgue and Wojciech Pieczynski},
  journal={IEEE Transactions on Automatic Control},
  year={2010},
  volume={55},
  pages={338-349}
}
Parametric modeling and estimation of non-Gaussian multidimensional probability density function is a difficult problem whose solution is required by many applications in signal and image processing. A lot of efforts have been devoted to escape the usual Gaussian assumption by developing perturbed Gaussian models such as spherically invariant random vectors (SIRVs). In this work, we introduce an alternative solution based on copulas that enables theoretically to represent any multivariate… 

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References

SHOWING 1-10 OF 60 REFERENCES
Copulas in vectorial hidden Markov chains for multicomponent image segmentation
  • N. Brunel, W. Pieczynski, S. Derrode
  • Computer Science, Mathematics
    Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005.
  • 2005
TLDR
This work introduces an alternative solution based on a very general class of multivariate models called 'copulas', which are used in the frame of multidimensional mixture estimation arising in the segmentation of multicomponent images, when using a vectorial hidden Markov chain (HMC).
Unsupervised signal restoration using hidden Markov chains with copulas
Estimation of Generalized Multisensor Hidden Markov Chains and Unsupervised Image Segmentation
TLDR
The proposed method is applied to the problem of unsupervised image segmentation and allows one to identify the conditional distribution for each class and each sensor, estimate the unknown parameters in this distribution, estimate priors, and estimate the "true" class image.
Non-Gaussian random vector identification using spherically invariant random processes
TLDR
E elegant and tractable techniques are presented for characterizing the probability density function (PDF) of a correlated non-Gaussian radar vector and an important result providing the PDF of the quadratic form of a spherically invariant random vector (SIRV) is presented.
The Meta-elliptical Distributions with Given Marginals
Based on an analysis of copulas of elliptically contoured distributions, joint densities of continuous variables with given strictly increasing marginal distributions are constructed. A method
Pairwise Markov Chains
  • W. Pieczynski
  • Computer Science, Mathematics
    IEEE Trans. Pattern Anal. Mach. Intell.
  • 2003
TLDR
An original method of parameter estimation, which generalizes the classical iterative conditional estimation (ICE) valid for a classical hidden Markov chain model, and whose extension to possibly non-Gaussian and correlated noise is briefly treated.
Unsupervised multiband image segmentation using hidden Markov quadtree and copulas
TLDR
A new approach based on copula theory to compute multivariate density on Markov quadtree for multiband image segmentation with real-time requirements is proposed.
Signal and image segmentation using pairwise Markov chains
TLDR
The main novelty is an original parameter estimation method that is valid in a general setting, where the form of the possibly correlated noise is not known, and with respect to the classical hidden Markov chain one for supervised and unsupervised restorations.
Non-Gaussian clutter modeling with generalized spherically invariant random vectors
TLDR
It is shown how applying this optimum detector to non-Gaussian data leads to a reduction in the false alarm rate when compared to processing with a matched filter alone.
Multisensor triplet Markov chains and theory of evidence
  • W. Pieczynski
  • Mathematics, Computer Science
    Int. J. Approx. Reason.
  • 2007
...
1
2
3
4
5
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