Parsimonious Higher-Order Hidden Markov Models for Improved Array-CGH Analysis with Applications to Arabidopsis thaliana

Array-based comparative genomic hybridization (Array-CGH) is an important technology in molecular biology for the detection of DNA copy number polymorphisms between closely related genomes. Hidden Markov Models (HMMs) are popular tools for the analysis of Array-CGH data, but current methods are only based on first-order HMMs having constrained abilities to model spatial dependencies between measurements of closely adjacent chromosomal regions. Here, we develop parsimonious higher-order HMMs enabling the interpolation between a mixture model ignoring spatial dependencies and a higher-order HMM exhaustively modeling spatial dependencies. We apply parsimonious higher-order HMMs to the analysis of Array-CGH data of the accessions C24 and Col-0 of the model plant Arabidopsis thaliana. We compare these models against first-order HMMs and other existing methods using a reference of known deletions and sequence deviations. We find that parsimonious higher-order HMMs clearly improve the identification of these polymorphisms. Moreover, we perform a functional analysis of identified polymorphisms revealing novel details of genomic differences between C24 and Col-0. Additional model evaluations are done on widely considered Array-CGH data of human cell lines indicating that parsimonious HMMs are also well-suited for the analysis of non-plant specific data. All these results indicate that parsimonious higher-order HMMs are useful for Array-CGH analyses. An implementation of parsimonious higher-order HMMs is available as part of the open source Java library Jstacs (www.jstacs.de/index.php/PHHMM)

Signal and Image Segmentation Using Pairwise Markov Chains

The aim of this paper is to apply the recent pairwise Markov chain model, which generalizes the hidden Markov chain one, to the unsupervised restoration of hidden data. The main novelty is an original parameter estimation method, valid in a general setting where the form of the possibly correlated noise is not known. Several experimental results are presented in both Gaussian and generalized mixture contexts. They show the advantages of the pairwise Markov chain model with respect to classical hidden Markov chain one for supervised and unsupervised restorations

CONTEXTUAL ESTIMATION OF HIDDEN MARKOV CHAINS WITH APPLICATION TO IMAGE SEGMENTATION

This paper presents a contextual algorithm for the computation of Baum’s forward and backward probabilities, which are intensively used in the framework of Hidden Markov Chain (HMC) models. The method differs from the original algorithm since it only takes into account a neighborhood of limited length and not all the chain for computations. Comparative experiments with respect to the neighborhood size have been conducted on both Markovian (simulations) and not Markovian (images) data, by mean of supervised and unsupervised classifications. 1

Unsupervised Image Segmentation Based on High-Order Hidden Markov Chains

First order hidden Markov models have been used for a long time in image processing, especially in image segmentation. In this paper, we propose a technique for the unsupervised segmentation of images, based on high-order hidden Markov chains. We also show that it is possible to relax the classical hypothesis regarding the state observation probability density, which allows to take into account some particular correlated noise. Model parameter estimation is performed from an extension of the general Iterative Conditional Estimation (ICE) method that takes into account the order of the chain. A comparative study conducted on a simulated image is carried out according to the order of the chain. Experimental results on Synthetic Aperture Radar (SAR) images show that the new approach can provide a more homogeneous segmentation than the classical one, implying higher complexity algorithm and computation time

Unsupervised Image Segmentation Based on a New Fuzzy HMC Model

In this paper, we propose a technique, based on a fuzzy Hidden Markov Chain (HMC) model, for the unsupervised segmentation of images. The main contribution of this work is to simultaneously use Dirac and Lebesgue measures at the class chain level. This model allows the coexistence of hard and fuzzy pixels in the same picture. In this way, the fuzzy approach enriches the classical model by adding a fuzzy class, which has several interpretations in signal processing. One such interpretation in image segmentation is the simultaneous appearance of several thematic classes on the same pixel (mixture). Model parameter estimation is performed through an extension of the Iterative Conditional Estimation (ICE) algorithm to take into account the fuzzy part. The fuzzy segmentation of a real image of clouds is studied and compared to the classification obtained with a "classical" hard HMC model